diff --git a/CompilerForCAP/examples/PrecompileModulePresentationsAsFreydCategoryOfCategoryOfRowsOrColumns.g b/CompilerForCAP/examples/PrecompileModulePresentationsAsFreydCategoryOfCategoryOfRowsOrColumns.g
index c5eb6d76f7..30693cd150 100644
--- a/CompilerForCAP/examples/PrecompileModulePresentationsAsFreydCategoryOfCategoryOfRowsOrColumns.g
+++ b/CompilerForCAP/examples/PrecompileModulePresentationsAsFreydCategoryOfCategoryOfRowsOrColumns.g
@@ -19,52 +19,52 @@ EEE := KoszulDualRing( QQxy * "a,b" );;
 operations_for_arbitrary_ring := [
     "AdditionForMorphisms",
     "AdditiveInverseForMorphisms",
-    #"AssociatorLeftToRightWithGivenTensorProducts",
-    #"AssociatorRightToLeftWithGivenTensorProducts",
-    #"BraidingWithGivenTensorProducts",
-    #"CoevaluationMorphismWithGivenRange",
     "CokernelColiftWithGivenCokernelObject",
     "CokernelProjection",
-    #"Colift",
-    #"ColiftOrFail",
     "DirectSum",
     "EpimorphismFromSomeProjectiveObject",
-    #"EvaluationMorphismWithGivenSource",
     "IdentityMorphism",
     "InjectionOfCofactorOfDirectSumWithGivenDirectSum",
-    #"InternalHomOnMorphismsWithGivenInternalHoms",
-    #"InternalHomOnObjects",
-    #"IsColiftable",
     "IsCongruentForMorphisms",
     "IsEqualForMorphisms",
-    #"IsEqualForObjects",
-    #"IsLiftable",
+    "IsEqualForObjects",
     #"IsWellDefinedForMorphisms",
     #"IsWellDefinedForObjects",
     "IsZeroForMorphisms",
-    #"KernelEmbedding",
-    #"LeftUnitorWithGivenTensorProduct",
-    #"Lift",
-    #"LiftAlongMonomorphism",
-    #"LiftOrFail",
-    #"MultiplyWithElementOfCommutativeRingForMorphisms",
-    #"PreCompose",
+    "KernelEmbedding",
+    "LiftAlongMonomorphism",
+    "PreCompose",
     "ProjectionInFactorOfDirectSumWithGivenDirectSum",
-    #"RightUnitorWithGivenTensorProduct",
-    #"TensorProductOnMorphismsWithGivenTensorProducts",
-    #"TensorProductOnObjects",
-    #"TensorUnit",
     "UniversalMorphismFromDirectSumWithGivenDirectSum",
     "UniversalMorphismFromZeroObjectWithGivenZeroObject",
     "UniversalMorphismIntoDirectSumWithGivenDirectSum",
     "UniversalMorphismIntoZeroObjectWithGivenZeroObject",
     "ZeroMorphism",
-    "ZeroObject" 
+    "ZeroObject",
 ];;
 
 operations_for_commutative_ring := Concatenation(
     operations_for_arbitrary_ring,
-    [ "MultiplyWithElementOfCommutativeRingForMorphisms" ]
+    [ "AssociatorLeftToRightWithGivenTensorProducts",
+      "AssociatorRightToLeftWithGivenTensorProducts",
+      "BraidingWithGivenTensorProducts",
+      "CoevaluationMorphismWithGivenRange",
+      #"Colift",
+      #"ColiftOrFail",
+      "EvaluationMorphismWithGivenSource",
+      "InternalHomOnMorphismsWithGivenInternalHoms",
+      "InternalHomOnObjects",
+      #"IsColiftable",
+      #"IsLiftable",
+      "LeftUnitorWithGivenTensorProduct",
+      #"Lift",
+      #"LiftOrFail",
+      "MultiplyWithElementOfCommutativeRingForMorphisms",
+      "RightUnitorWithGivenTensorProduct",
+      "TensorProductOnMorphismsWithGivenTensorProducts",
+      "TensorProductOnObjects",
+      "TensorUnit",
+    ]
 );;
 
 precompile_LeftPresentations := function( ring, name, operations )
diff --git a/CompilerForCAP/gap/InferDataTypes.gi b/CompilerForCAP/gap/InferDataTypes.gi
index fd9be5a77f..5c198a3fa6 100644
--- a/CompilerForCAP/gap/InferDataTypes.gi
+++ b/CompilerForCAP/gap/InferDataTypes.gi
@@ -1461,8 +1461,14 @@ CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "CertainRows", [ "IsHomalgM
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "CertainColumns", [ "IsHomalgMatrix", "IsList" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "KroneckerMat", [ "IsHomalgMatrix", "IsHomalgMatrix" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "DualKroneckerMat", [ "IsHomalgMatrix", "IsHomalgMatrix" ], "IsHomalgMatrix" );
+CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "BasisOfRowModule", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
+CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "BasisOfColumnModule", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
+CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "ReducedBasisOfRowModule", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
+CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "ReducedBasisOfColumnModule", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "LeftDivide", [ "IsHomalgMatrix", "IsHomalgMatrix" ], "IsHomalgMatrix" );
+CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "LeftDivide", [ "IsHomalgMatrix", "IsHomalgMatrix", "IsHomalgMatrix" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "RightDivide", [ "IsHomalgMatrix", "IsHomalgMatrix" ], "IsHomalgMatrix" );
+CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "RightDivide", [ "IsHomalgMatrix", "IsHomalgMatrix", "IsHomalgMatrix" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "BasisOfRows", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "BasisOfColumns", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
 CapJitAddTypeSignatureDeferred( "MatricesForHomalg", "SyzygiesOfRows", [ "IsHomalgMatrix" ], "IsHomalgMatrix" );
diff --git a/FreydCategoriesForCAP/gap/FreydCategory.gd b/FreydCategoriesForCAP/gap/FreydCategory.gd
index f520743f06..a7262f0ca3 100644
--- a/FreydCategoriesForCAP/gap/FreydCategory.gd
+++ b/FreydCategoriesForCAP/gap/FreydCategory.gd
@@ -237,7 +237,7 @@ DeclareGlobalFunction( "IsValidInputForFreydCategory" );
 #! into $\mathrm{\underline{Hom}}(A, b)$ is the internal Hom-embedding. This method returns this very map.
 #! @Returns a (mono)morphism
 #! @Arguments cat, a, b
-DeclareOperationWithCache( "INTERNAL_HOM_EMBEDDING",
+DeclareOperation( "INTERNAL_HOM_EMBEDDING",
                            [ IsFreydCategory, IsFreydCategoryObject, IsFreydCategoryObject ] );
 
 
diff --git a/FreydCategoriesForCAP/gap/FreydCategory.gi b/FreydCategoriesForCAP/gap/FreydCategory.gi
index fc694a8305..a40ebfbb3c 100644
--- a/FreydCategoriesForCAP/gap/FreydCategory.gi
+++ b/FreydCategoriesForCAP/gap/FreydCategory.gi
@@ -337,7 +337,7 @@ InstallOtherMethodForCompilerForCAP( MereExistenceOfWitnessForBeingCongruentToZe
     
 end );
 
-InstallMethodWithCacheFromObject( INTERNAL_HOM_EMBEDDING,
+InstallMethodForCompilerForCAP( INTERNAL_HOM_EMBEDDING,
                                   [ IsFreydCategory, IsFreydCategoryObject, IsFreydCategoryObject ],
     function( cat, a, b )
       local source, range, mor;
diff --git a/LinearAlgebraForCAP/gap/CompilerLogic.gi b/LinearAlgebraForCAP/gap/CompilerLogic.gi
index 5e0e1a81cd..11c5422bb3 100644
--- a/LinearAlgebraForCAP/gap/CompilerLogic.gi
+++ b/LinearAlgebraForCAP/gap/CompilerLogic.gi
@@ -54,3 +54,329 @@ CapJitAddLogicTemplate(
         needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
     )
 );
+
+# TransposedMatrix( HomalgIdentityMatrix( size, ring ) ) -> HomalgIdentityMatrix( size, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "ring" ],
+        src_template := "TransposedMatrix( HomalgIdentityMatrix( size, ring ) )",
+        dst_template := "HomalgIdentityMatrix( size, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# TransposedMatrix( HomalgZeroMatrix( 0, size, ring ) ) -> HomalgZeroMatrix( size, 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "ring" ],
+        src_template := "TransposedMatrix( HomalgZeroMatrix( 0, size, ring ) )",
+        dst_template := "HomalgZeroMatrix( size, 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# TransposedMatrix( HomalgZeroMatrix( size, 0, ring ) ) -> HomalgZeroMatrix( 0, size, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "ring" ],
+        src_template := "TransposedMatrix( HomalgZeroMatrix( size, 0, ring ) )",
+        dst_template := "HomalgZeroMatrix( 0, size, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( HomalgZeroMatrix( size, 0, ring ), matrix ) -> HomalgZeroMatrix( size * NumberRows( matrix ), 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "matrix", "ring" ],
+        src_template := "KroneckerMat( HomalgZeroMatrix( size, 0, ring ), matrix )",
+        dst_template := "HomalgZeroMatrix( size * NumberRows( matrix ), 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( HomalgZeroMatrix( 0, size, ring ), matrix ) -> HomalgZeroMatrix( 0, size * NumberColumns( matrix ), ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "matrix", "ring" ],
+        src_template := "KroneckerMat( HomalgZeroMatrix( 0, size, ring ), matrix )",
+        dst_template := "HomalgZeroMatrix( 0, size * NumberColumns( matrix ), ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( matrix, HomalgZeroMatrix( size, 0, ring ) ) -> HomalgZeroMatrix( NumberRows( matrix ) * size, 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "matrix", "ring" ],
+        src_template := "KroneckerMat( matrix, HomalgZeroMatrix( size, 0, ring ) )",
+        dst_template := "HomalgZeroMatrix( NumberRows( matrix ) * size, 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( matrix, HomalgZeroMatrix( 0, size, ring ) ) -> HomalgZeroMatrix( 0, NumberColumns( matrix ) * size, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "size", "matrix", "ring" ],
+        src_template := "KroneckerMat( matrix, HomalgZeroMatrix( 0, size, ring ) )",
+        dst_template := "HomalgZeroMatrix( 0, NumberColumns( matrix ) * size, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( HomalgIdentityMatrix( 0, ring ), matrix ) -> HomalgIdentityMatrix( 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "ring" ],
+        src_template := "KroneckerMat( HomalgIdentityMatrix( 0, ring ), matrix )",
+        dst_template := "HomalgIdentityMatrix( 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( matrix, HomalgIdentityMatrix( 0, ring ) ) -> HomalgIdentityMatrix( 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "ring" ],
+        src_template := "KroneckerMat( matrix, HomalgIdentityMatrix( 0, ring ) )",
+        dst_template := "HomalgIdentityMatrix( 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# KroneckerMat( HomalgIdentityMatrix( m, ring ) , HomalgIdentityMatrix( n ring ) ) -> HomalgIdentityMatrix( m*n, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "m", "n", "ring" ],
+        src_template := "KroneckerMat( HomalgIdentityMatrix( m, ring ), HomalgIdentityMatrix( n, ring ) )",
+        dst_template := "HomalgIdentityMatrix( m*n, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# TODO?
+# KroneckerMat( HomalgIdentityMatrix( m, ring ), matrix ) -> DiagMat( ring, ListWithIdenticalEntries( m, matrix ) )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "m", "matrix", "ring" ],
+        src_template := "KroneckerMat( HomalgIdentityMatrix( m, ring ), matrix )",
+        dst_template := "DiagMat( ring, ListWithIdenticalEntries( m, matrix ) )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# DiagMat( ring, [ ] ) -> HomalgIdentityMatrix( 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "ring" ],
+        src_template := "DiagMat( ring, [ ] )",
+        dst_template := "HomalgIdentityMatrix( 0, ring )",
+    )
+);
+
+# ReducedSyzygiesOfRows( matrix, HomalgIdentityMatrix( 0, ring ) ) -> ReducedSyzygiesOfRows( matrix )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "ring" ],
+        src_template := "ReducedSyzygiesOfRows( matrix, HomalgIdentityMatrix( 0, ring ) )",
+        dst_template := "ReducedSyzygiesOfRows( matrix )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfColumns( matrix, HomalgIdentityMatrix( 0, ring ) ) -> ReducedSyzygiesOfColumns( matrix )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "ring" ],
+        src_template := "ReducedSyzygiesOfColumns( matrix, HomalgIdentityMatrix( 0, ring ) )",
+        dst_template := "ReducedSyzygiesOfColumns( matrix )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfRows( matrix, HomalgZeroMatrix( m, n, ring ) ) -> ReducedSyzygiesOfRows( matrix )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "m", "n", "ring" ],
+        src_template := "ReducedSyzygiesOfRows( matrix, HomalgZeroMatrix( m, n, ring ) )",
+        dst_template := "ReducedSyzygiesOfRows( matrix )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfColumns( matrix, HomalgZeroMatrix( m, n, ring ) ) -> ReducedSyzygiesOfColumns( matrix )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "m", "n", "ring" ],
+        src_template := "ReducedSyzygiesOfColumns( matrix, HomalgZeroMatrix( m, n, ring ) )",
+        dst_template := "ReducedSyzygiesOfColumns( matrix )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfRows( HomalgZeroMatrix( 0, m, ring ) ) -> HomalgZeroMatrix( 0, 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "m", "ring" ],
+        src_template := "ReducedSyzygiesOfRows( HomalgZeroMatrix( 0, m, ring ) )",
+        dst_template := "HomalgZeroMatrix( 0, 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfRows( HomalgZeroMatrix( m, 0, ring ) ) -> HomalgIdentityMatrix( m, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "m", "ring" ],
+        src_template := "ReducedSyzygiesOfRows( HomalgZeroMatrix( m, 0, ring ) )",
+        dst_template := "HomalgIdentityMatrix( m, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfColumns( HomalgZeroMatrix( 0, m, ring ) ) -> HomalgIdentityMatrix( m, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "m", "ring" ],
+        src_template := "ReducedSyzygiesOfColumns( HomalgZeroMatrix( 0, m, ring ) )",
+        dst_template := "HomalgIdentityMatrix( m, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# ReducedSyzygiesOfColumns( HomalgZeroMatrix( m, 0, ring ) ) -> HomalgZeroMatrix( 0, 0, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "m", "ring" ],
+        src_template := "ReducedSyzygiesOfColumns( HomalgZeroMatrix( m, 0, ring ) )",
+        dst_template := "HomalgZeroMatrix( 0, 0, ring )",
+        needed_packages := [ [ "MatricesForHomalg", ">= 2020.05.19" ] ],
+    )
+);
+
+# TODO
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix_B", "matrix_A", "matrix_L", "ring", "nr_cols_A", "nr_rows_L" ],
+        src_template := "CertainColumns( RightDivide( matrix_B, UnionOfRows( ring, nr_cols_A, [ matrix_L, matrix_A ] ) ), [ NumberRows( matrix_L ) + 1 .. NumberRows( matrix_L ) + 1 - 1 + nr_rows_L ] ) ",
+        dst_template := "RightDivide( matrix_B, matrix_A, matrix_L )",
+    )
+);
+
+# TODO
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix_A", "matrix_B", "matrix_L", "ring", "nr_rows_A", "nr_cols_L" ],
+        src_template := "CertainRows( LeftDivide( UnionOfColumns( ring, nr_rows_A, [ matrix_L, matrix_A ] ), matrix_B ), [ NumberColumns( matrix_L ) + 1 .. NumberColumns( matrix_L ) + 1 - 1 + nr_cols_L ] )",
+        dst_template := "LeftDivide( matrix_A, matrix_B, matrix_L )",
+    )
+);
+
+# RightDivide( HomalgIdentityMatrix( number, ring ), HomalgIdentityMatrix( number, ring ), matrix_L ) -> HomalgIdentityMatrix( number, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix_L", "ring", "number" ],
+        src_template := "RightDivide( HomalgIdentityMatrix( number, ring ), HomalgIdentityMatrix( number, ring ), matrix_L )",
+        dst_template := "HomalgIdentityMatrix( number, ring )",
+    )
+);
+
+# LeftDivide( HomalgIdentityMatrix( number, ring ), HomalgIdentityMatrix( number, ring ), matrix_L ) -> HomalgIdentityMatrix( number, ring )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix_L", "ring", "number" ],
+        src_template := "LeftDivide( HomalgIdentityMatrix( number, ring ), HomalgIdentityMatrix( number, ring ), matrix_L )",
+        dst_template := "HomalgIdentityMatrix( number, ring )",
+    )
+);
+
+# ReducedSyzygiesOfRows( HomalgIdentityMatrix( number, ring ), M2 ) -> ReducedBasisOfRowModule( M2 )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "M2", "ring", "number" ],
+        src_template := "ReducedSyzygiesOfRows( HomalgIdentityMatrix( number, ring ), M2 )",
+        dst_template := "ReducedBasisOfRowModule( M2 )",
+    )
+);
+
+# ReducedSyzygiesOfColumns( HomalgIdentityMatrix( number, ring ), M2 ) -> ReducedBasisOfColumnModule( M2 )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "M2", "ring", "number" ],
+        src_template := "ReducedSyzygiesOfColumns( HomalgIdentityMatrix( number, ring ), M2 )",
+        dst_template := "ReducedBasisOfColumnModule( M2 )",
+    )
+);
+
+# ReducedBasisOfRowModule( DiagMat( ring, ListWithIdenticalEntries( number, matrix ) ) ) -> DiagMat( ring, ListWithIdenticalEntries( number, ReducedBasisOfRowModule( matrix ) ) )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "ring", "number" ],
+        src_template := "ReducedBasisOfRowModule( DiagMat( ring, ListWithIdenticalEntries( number, matrix ) ) )",
+        dst_template := "DiagMat( ring, ListWithIdenticalEntries( number, ReducedBasisOfRowModule( matrix ) ) )",
+    )
+);
+
+# ReducedBasisOfColumnModule( DiagMat( ring, ListWithIdenticalEntries( number, matrix ) ) ) -> DiagMat( ring, ListWithIdenticalEntries( number, ReducedBasisOfColumnModule( matrix ) ) )
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "matrix", "ring", "number" ],
+        src_template := "ReducedBasisOfColumnModule( DiagMat( ring, ListWithIdenticalEntries( number, matrix ) ) )",
+        dst_template := "DiagMat( ring, ListWithIdenticalEntries( number, ReducedBasisOfColumnModule( matrix ) ) )",
+    )
+);
+
+# ListWithIdenticalEntries( 0, a ) = [ ]
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "a" ],
+        src_template := "ListWithIdenticalEntries( 0, a )",
+        dst_template := "[ ]",
+    )
+);
+
+# [ 1 .. 2 - 1 ] -> [ 1 ]
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ ],
+        src_template := "[ 1 .. 2 - 1 ]",
+        dst_template := "[ 1 ]",
+    )
+);
+
+# [ a, b ]{ [ 1 ] } -> [ a ]
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "a", "b" ],
+        src_template := "[ a, b ]{ [ 1 ] }",
+        dst_template := "[ a ]",
+    )
+);
+
+# Sum( [ a ] ) -> a
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "a" ],
+        src_template := "Sum( [ a ] )",
+        dst_template := "a",
+    )
+);
+
+# 0 * a = 0
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "a" ],
+        src_template := "0 * a",
+        dst_template := "0",
+    )
+);
+
+# a * 0 = 0
+CapJitAddLogicTemplate(
+    rec(
+        variable_names := [ "a" ],
+        src_template := "a * 0",
+        dst_template := "0",
+    )
+);
diff --git a/LinearAlgebraForCAP/gap/precompiled_categories/MatrixCategoryPrecompiled.gi b/LinearAlgebraForCAP/gap/precompiled_categories/MatrixCategoryPrecompiled.gi
index 65ebd579eb..361a9c4cfd 100644
--- a/LinearAlgebraForCAP/gap/precompiled_categories/MatrixCategoryPrecompiled.gi
+++ b/LinearAlgebraForCAP/gap/precompiled_categories/MatrixCategoryPrecompiled.gi
@@ -253,48 +253,46 @@ end
         
 ########
 function ( cat_1, a_1, b_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1;
-    deduped_21_1 := UnderlyingRing( cat_1 );
-    deduped_20_1 := Dimension( b_1 );
-    deduped_19_1 := Dimension( a_1 );
-    deduped_18_1 := 1 * deduped_19_1;
-    deduped_17_1 := HomalgIdentityMatrix( deduped_19_1, deduped_21_1 );
-    deduped_16_1 := 1 * deduped_20_1;
-    deduped_15_1 := HomalgIdentityMatrix( deduped_20_1, deduped_21_1 );
-    deduped_14_1 := HomalgIdentityMatrix( 1, deduped_21_1 );
-    deduped_13_1 := deduped_19_1 * deduped_20_1;
-    deduped_12_1 := deduped_13_1 * deduped_13_1;
-    deduped_11_1 := deduped_18_1 * deduped_16_1;
-    deduped_10_1 := deduped_19_1 * deduped_16_1;
-    deduped_9_1 := HomalgIdentityMatrix( deduped_13_1, deduped_21_1 );
-    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_21_1 );
-    deduped_7_1 := deduped_11_1 * deduped_13_1;
-    hoisted_6_1 := deduped_11_1;
-    hoisted_5_1 := deduped_13_1;
-    hoisted_4_1 := deduped_16_1;
-    hoisted_3_1 := deduped_19_1;
-    hoisted_2_1 := deduped_20_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_9_1 ), KroneckerMat( deduped_14_1, KroneckerMat( deduped_14_1, ConvertMatrixToRow( deduped_15_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1;
+    deduped_19_1 := Dimension( b_1 );
+    deduped_18_1 := Dimension( a_1 );
+    deduped_17_1 := UnderlyingRing( cat_1 );
+    deduped_16_1 := 1 * deduped_18_1;
+    deduped_15_1 := HomalgIdentityMatrix( deduped_18_1, deduped_17_1 );
+    deduped_14_1 := 1 * deduped_19_1;
+    deduped_13_1 := HomalgIdentityMatrix( deduped_19_1, deduped_17_1 );
+    deduped_12_1 := deduped_18_1 * deduped_19_1;
+    deduped_11_1 := deduped_12_1 * deduped_12_1;
+    deduped_10_1 := deduped_16_1 * deduped_14_1;
+    deduped_9_1 := deduped_18_1 * deduped_14_1;
+    deduped_8_1 := HomalgIdentityMatrix( deduped_10_1, deduped_17_1 );
+    deduped_7_1 := deduped_10_1 * deduped_12_1;
+    hoisted_6_1 := deduped_10_1;
+    hoisted_5_1 := deduped_12_1;
+    hoisted_4_1 := deduped_14_1;
+    hoisted_3_1 := deduped_18_1;
+    hoisted_2_1 := deduped_19_1;
+    morphism_attr_1_1 := DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_12_1, DiagMat( deduped_17_1, ListWithIdenticalEntries( 1, DiagMat( deduped_17_1, ListWithIdenticalEntries( 1, ConvertMatrixToRow( deduped_13_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                                end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_21_1 ), deduped_15_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_20_1 * 1), deduped_21_1 ), deduped_15_1 ) ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_14_1, ConvertMatrixToRow( deduped_17_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                      local deduped_1_2;
-                                      deduped_1_2 := (i_2 - 1);
-                                      return (REM_INT( deduped_1_2, hoisted_3_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                                  end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_21_1 ), deduped_17_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_19_1 * 1), deduped_21_1 ), deduped_17_1 )), HomalgIdentityMatrix( deduped_16_1, deduped_21_1 ) ), deduped_15_1 ) * KroneckerMat( KroneckerMat( HomalgIdentityMatrix( deduped_18_1, deduped_21_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_21_1 ) ), deduped_15_1 ) ) * (KroneckerMat( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                                end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_17_1 ), deduped_13_1 ) ) ) * KroneckerMat( KroneckerMat( (DiagMat( deduped_17_1, ListWithIdenticalEntries( 1, ConvertMatrixToRow( deduped_15_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                    local deduped_1_2;
+                                    deduped_1_2 := (i_2 - 1);
+                                    return (REM_INT( deduped_1_2, hoisted_3_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                                end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_17_1 ), deduped_15_1 )), HomalgIdentityMatrix( deduped_14_1, deduped_17_1 ) ), deduped_13_1 ) * KroneckerMat( DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_16_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                            end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_17_1 ) ) ), deduped_13_1 ) ) ) * (DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_21_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                        end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_21_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_9_1 ), deduped_8_1 )) * KroneckerMat( deduped_17_1, deduped_15_1 );
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_17_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
+                      end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_17_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_12_1, deduped_17_1 ) ), deduped_8_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -306,48 +304,46 @@ end
         
 ########
 function ( cat_1, s_1, a_1, b_1, r_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1;
-    deduped_21_1 := UnderlyingRing( cat_1 );
-    deduped_20_1 := Dimension( b_1 );
-    deduped_19_1 := Dimension( a_1 );
-    deduped_18_1 := 1 * deduped_19_1;
-    deduped_17_1 := HomalgIdentityMatrix( deduped_19_1, deduped_21_1 );
-    deduped_16_1 := 1 * deduped_20_1;
-    deduped_15_1 := HomalgIdentityMatrix( deduped_20_1, deduped_21_1 );
-    deduped_14_1 := HomalgIdentityMatrix( 1, deduped_21_1 );
-    deduped_13_1 := deduped_19_1 * deduped_20_1;
-    deduped_12_1 := deduped_13_1 * deduped_13_1;
-    deduped_11_1 := deduped_18_1 * deduped_16_1;
-    deduped_10_1 := deduped_19_1 * deduped_16_1;
-    deduped_9_1 := HomalgIdentityMatrix( deduped_13_1, deduped_21_1 );
-    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_21_1 );
-    deduped_7_1 := deduped_11_1 * deduped_13_1;
-    hoisted_6_1 := deduped_11_1;
-    hoisted_5_1 := deduped_13_1;
-    hoisted_4_1 := deduped_16_1;
-    hoisted_3_1 := deduped_19_1;
-    hoisted_2_1 := deduped_20_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_9_1 ), KroneckerMat( deduped_14_1, KroneckerMat( deduped_14_1, ConvertMatrixToRow( deduped_15_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1;
+    deduped_19_1 := Dimension( b_1 );
+    deduped_18_1 := Dimension( a_1 );
+    deduped_17_1 := UnderlyingRing( cat_1 );
+    deduped_16_1 := 1 * deduped_18_1;
+    deduped_15_1 := HomalgIdentityMatrix( deduped_18_1, deduped_17_1 );
+    deduped_14_1 := 1 * deduped_19_1;
+    deduped_13_1 := HomalgIdentityMatrix( deduped_19_1, deduped_17_1 );
+    deduped_12_1 := deduped_18_1 * deduped_19_1;
+    deduped_11_1 := deduped_12_1 * deduped_12_1;
+    deduped_10_1 := deduped_16_1 * deduped_14_1;
+    deduped_9_1 := deduped_18_1 * deduped_14_1;
+    deduped_8_1 := HomalgIdentityMatrix( deduped_10_1, deduped_17_1 );
+    deduped_7_1 := deduped_10_1 * deduped_12_1;
+    hoisted_6_1 := deduped_10_1;
+    hoisted_5_1 := deduped_12_1;
+    hoisted_4_1 := deduped_14_1;
+    hoisted_3_1 := deduped_18_1;
+    hoisted_2_1 := deduped_19_1;
+    morphism_attr_1_1 := DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_12_1, DiagMat( deduped_17_1, ListWithIdenticalEntries( 1, DiagMat( deduped_17_1, ListWithIdenticalEntries( 1, ConvertMatrixToRow( deduped_13_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                                end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_21_1 ), deduped_15_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_20_1 * 1), deduped_21_1 ), deduped_15_1 ) ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_14_1, ConvertMatrixToRow( deduped_17_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                      local deduped_1_2;
-                                      deduped_1_2 := (i_2 - 1);
-                                      return (REM_INT( deduped_1_2, hoisted_3_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                                  end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_21_1 ), deduped_17_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_19_1 * 1), deduped_21_1 ), deduped_17_1 )), HomalgIdentityMatrix( deduped_16_1, deduped_21_1 ) ), deduped_15_1 ) * KroneckerMat( KroneckerMat( HomalgIdentityMatrix( deduped_18_1, deduped_21_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_21_1 ) ), deduped_15_1 ) ) * (KroneckerMat( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                                end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_17_1 ), deduped_13_1 ) ) ) * KroneckerMat( KroneckerMat( (DiagMat( deduped_17_1, ListWithIdenticalEntries( 1, ConvertMatrixToRow( deduped_15_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                    local deduped_1_2;
+                                    deduped_1_2 := (i_2 - 1);
+                                    return (REM_INT( deduped_1_2, hoisted_3_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                                end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_17_1 ), deduped_15_1 )), HomalgIdentityMatrix( deduped_14_1, deduped_17_1 ) ), deduped_13_1 ) * KroneckerMat( DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_16_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                            end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_17_1 ) ) ), deduped_13_1 ) ) ) * (DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_21_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                        end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_21_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_9_1 ), deduped_8_1 )) * KroneckerMat( deduped_17_1, deduped_15_1 );
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_17_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
+                      end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_17_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_12_1, deduped_17_1 ) ), deduped_8_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -361,17 +357,17 @@ end
 function ( cat_1, a_1, b_1, alpha_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := UnderlyingRing( cat_1 );
-    deduped_6_1 := Dimension( a_1 );
-    deduped_5_1 := deduped_6_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_7_1 );
-    hoisted_3_1 := deduped_6_1;
+    deduped_7_1 := Dimension( a_1 );
+    deduped_6_1 := UnderlyingRing( cat_1 );
+    deduped_5_1 := deduped_7_1 * deduped_8_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_6_1 );
+    hoisted_3_1 := deduped_7_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_6_1, deduped_7_1 ), ConvertMatrixToRow( deduped_4_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_8_1 * deduped_6_1), deduped_7_1 ), deduped_4_1 ) * KroneckerMat( UnderlyingMatrix( alpha_1 ), deduped_4_1 );
+    morphism_attr_1_1 := DiagMat( deduped_6_1, ListWithIdenticalEntries( deduped_7_1, ConvertMatrixToRow( deduped_4_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( UnderlyingMatrix( alpha_1 ), deduped_4_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), b_1, UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -383,23 +379,22 @@ end
         
 ########
 function ( cat_1, alpha_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := UnderlyingRing( cat_1 );
-    deduped_7_1 := HomalgIdentityMatrix( 1, deduped_8_1 );
-    deduped_6_1 := Dimension( Range( alpha_1 ) );
-    deduped_5_1 := deduped_6_1 * deduped_6_1;
-    deduped_4_1 := 1 * deduped_6_1;
-    deduped_3_1 := HomalgIdentityMatrix( deduped_6_1, deduped_8_1 );
-    hoisted_2_1 := deduped_6_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_3_1 ), UnderlyingMatrix( alpha_1 ) ) * (KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( 1, deduped_7_1 );
+    deduped_5_1 := Dimension( Range( alpha_1 ) );
+    deduped_4_1 := deduped_5_1 * deduped_5_1;
+    deduped_3_1 := 1 * deduped_5_1;
+    hoisted_2_1 := deduped_5_1;
+    morphism_attr_1_1 := DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_5_1, UnderlyingMatrix( alpha_1 ) ) ) * (DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_5_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                        end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_3_1 ), deduped_7_1 ));
+                      end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ), deduped_6_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_5_1, deduped_7_1 ) ), deduped_6_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -419,11 +414,11 @@ function ( cat_1, a_1 )
     deduped_4_1 := 1 * deduped_7_1;
     deduped_3_1 := HomalgIdentityMatrix( deduped_7_1, deduped_8_1 );
     hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := ConvertMatrixToRow( deduped_3_1 ) * (KroneckerMat( TransposedMatrix( deduped_3_1 ), deduped_3_1 ) * (KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    morphism_attr_1_1 := ConvertMatrixToRow( deduped_3_1 ) * (DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, deduped_3_1 ) ) * (DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                              local deduped_1_2;
+                              deduped_1_2 := (i_2 - 1);
+                              return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                          end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
@@ -439,23 +434,22 @@ end
         
 ########
 function ( cat_1, alpha_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := UnderlyingRing( cat_1 );
-    deduped_7_1 := HomalgIdentityMatrix( 1, deduped_8_1 );
-    deduped_6_1 := Dimension( Range( alpha_1 ) );
-    deduped_5_1 := deduped_6_1 * deduped_6_1;
-    deduped_4_1 := 1 * deduped_6_1;
-    deduped_3_1 := HomalgIdentityMatrix( deduped_6_1, deduped_8_1 );
-    hoisted_2_1 := deduped_6_1;
-    morphism_attr_1_1 := ConvertMatrixToRow( HomalgIdentityMatrix( Dimension( Source( alpha_1 ) ), deduped_8_1 ) ) * (KroneckerMat( TransposedMatrix( deduped_3_1 ), UnderlyingMatrix( alpha_1 ) ) * (KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( 1, deduped_7_1 );
+    deduped_5_1 := Dimension( Range( alpha_1 ) );
+    deduped_4_1 := deduped_5_1 * deduped_5_1;
+    deduped_3_1 := 1 * deduped_5_1;
+    hoisted_2_1 := deduped_5_1;
+    morphism_attr_1_1 := ConvertMatrixToRow( HomalgIdentityMatrix( Dimension( Source( alpha_1 ) ), deduped_7_1 ) ) * (DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_5_1, UnderlyingMatrix( alpha_1 ) ) ) * (DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_5_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                              local deduped_1_2;
+                              deduped_1_2 := (i_2 - 1);
+                              return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                          end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_3_1 ), deduped_7_1 )));
+                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ), deduped_6_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_5_1, deduped_7_1 ) ), deduped_6_1 )));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -518,25 +512,24 @@ end
         
 ########
 function ( cat_1, a_1, b_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( a_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( a_1 );
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := deduped_10_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( deduped_9_1, deduped_7_1 );
+    deduped_5_1 := deduped_8_1 * deduped_8_1;
+    deduped_4_1 := deduped_9_1 * deduped_8_1;
+    hoisted_3_1 := deduped_9_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_9_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                      end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_4_1 ), deduped_7_1 );
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_6_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_8_1, deduped_7_1 ) ), deduped_6_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -548,25 +541,24 @@ end
         
 ########
 function ( cat_1, a_1, b_1, s_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( a_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( a_1 );
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := deduped_10_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( deduped_9_1, deduped_7_1 );
+    deduped_5_1 := deduped_8_1 * deduped_8_1;
+    deduped_4_1 := deduped_9_1 * deduped_8_1;
+    hoisted_3_1 := deduped_9_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_9_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                      end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_4_1 ), deduped_7_1 );
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_6_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_8_1, deduped_7_1 ) ), deduped_6_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -604,17 +596,17 @@ end
 function ( cat_1, a_1, b_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := UnderlyingRing( cat_1 );
-    deduped_6_1 := Dimension( a_1 );
-    deduped_5_1 := deduped_6_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_7_1 );
-    hoisted_3_1 := deduped_6_1;
+    deduped_7_1 := Dimension( a_1 );
+    deduped_6_1 := UnderlyingRing( cat_1 );
+    deduped_5_1 := deduped_7_1 * deduped_8_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_6_1 );
+    hoisted_3_1 := deduped_7_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_6_1, deduped_7_1 ), ConvertMatrixToRow( deduped_4_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_8_1 * deduped_6_1), deduped_7_1 ), deduped_4_1 );
+    morphism_attr_1_1 := DiagMat( deduped_6_1, ListWithIdenticalEntries( deduped_7_1, ConvertMatrixToRow( deduped_4_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                  end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ), deduped_4_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -628,17 +620,17 @@ end
 function ( cat_1, a_1, b_1, r_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := UnderlyingRing( cat_1 );
-    deduped_6_1 := Dimension( a_1 );
-    deduped_5_1 := deduped_6_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_7_1 );
-    hoisted_3_1 := deduped_6_1;
+    deduped_7_1 := Dimension( a_1 );
+    deduped_6_1 := UnderlyingRing( cat_1 );
+    deduped_5_1 := deduped_7_1 * deduped_8_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_6_1 );
+    hoisted_3_1 := deduped_7_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_6_1, deduped_7_1 ), ConvertMatrixToRow( deduped_4_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_8_1 * deduped_6_1), deduped_7_1 ), deduped_4_1 );
+    morphism_attr_1_1 := DiagMat( deduped_6_1, ListWithIdenticalEntries( deduped_7_1, ConvertMatrixToRow( deduped_4_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                  end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ), deduped_4_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -685,25 +677,24 @@ end
         
 ########
 function ( cat_1, a_1, b_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( a_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
-    deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := deduped_8_1 * deduped_10_1;
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
-    hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_4_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( a_1 );
+    deduped_8_1 := UnderlyingRing( cat_1 );
+    deduped_7_1 := Dimension( b_1 );
+    deduped_6_1 := deduped_7_1 * deduped_9_1;
+    deduped_5_1 := deduped_7_1 * deduped_7_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_9_1, deduped_8_1 );
+    hoisted_3_1 := deduped_9_1;
+    hoisted_2_1 := deduped_7_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_7_1, deduped_8_1 ) ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_5_1 ) * KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                      local deduped_1_2;
-                      deduped_1_2 := (i_2 - 1);
-                      return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                  end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_9_1 ) );
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_4_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                    end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_8_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -715,25 +706,24 @@ end
         
 ########
 function ( cat_1, a_1, b_1, r_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( a_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
-    deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := deduped_8_1 * deduped_10_1;
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
-    hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_4_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( a_1 );
+    deduped_8_1 := UnderlyingRing( cat_1 );
+    deduped_7_1 := Dimension( b_1 );
+    deduped_6_1 := deduped_7_1 * deduped_9_1;
+    deduped_5_1 := deduped_7_1 * deduped_7_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_9_1, deduped_8_1 );
+    hoisted_3_1 := deduped_9_1;
+    hoisted_2_1 := deduped_7_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_7_1, deduped_8_1 ) ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_5_1 ) * KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                      local deduped_1_2;
-                      deduped_1_2 := (i_2 - 1);
-                      return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                  end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_9_1 ) );
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_4_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                    end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_8_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -1272,11 +1262,11 @@ function ( cat_1, a_1, b_1 )
     deduped_4_1 := deduped_6_1 * deduped_7_1;
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_4_1, deduped_8_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_5_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_7_1, deduped_8_1 ), ConvertMatrixToColumn( deduped_5_1 ) );
+    morphism_attr_1_1 := KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                  end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_5_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, ConvertMatrixToColumn( deduped_5_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -1296,11 +1286,11 @@ function ( cat_1, a_1, b_1, s_1 )
     deduped_4_1 := deduped_6_1 * deduped_7_1;
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_4_1, deduped_8_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_5_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_7_1, deduped_8_1 ), ConvertMatrixToColumn( deduped_5_1 ) );
+    morphism_attr_1_1 := KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                  end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_5_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, ConvertMatrixToColumn( deduped_5_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -1798,53 +1788,51 @@ end
         
 ########
 function ( cat_1, list_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1;
-    deduped_26_1 := UnderlyingRing( cat_1 );
-    deduped_25_1 := List( list_1, Dimension );
-    deduped_24_1 := deduped_25_1[2];
-    deduped_23_1 := deduped_25_1[1];
-    deduped_22_1 := deduped_25_1[4];
-    deduped_21_1 := deduped_25_1[3];
-    deduped_20_1 := deduped_23_1 * deduped_21_1;
-    deduped_19_1 := HomalgIdentityMatrix( deduped_21_1, deduped_26_1 );
-    deduped_18_1 := deduped_24_1 * deduped_22_1;
-    deduped_17_1 := HomalgIdentityMatrix( deduped_22_1, deduped_26_1 );
-    deduped_16_1 := HomalgIdentityMatrix( deduped_23_1, deduped_26_1 );
-    deduped_15_1 := deduped_21_1 * deduped_22_1;
-    deduped_14_1 := deduped_15_1 * deduped_15_1;
-    deduped_13_1 := deduped_20_1 * deduped_18_1;
-    deduped_12_1 := deduped_21_1 * deduped_18_1;
-    deduped_11_1 := HomalgIdentityMatrix( deduped_15_1, deduped_26_1 );
-    deduped_10_1 := HomalgIdentityMatrix( deduped_13_1, deduped_26_1 );
-    deduped_9_1 := deduped_13_1 * deduped_15_1;
-    hoisted_8_1 := deduped_13_1;
-    hoisted_7_1 := deduped_15_1;
-    hoisted_6_1 := deduped_18_1;
-    hoisted_5_1 := deduped_23_1;
-    hoisted_4_1 := deduped_21_1;
-    hoisted_3_1 := deduped_24_1;
-    hoisted_2_1 := deduped_22_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_11_1 ), KroneckerMat( deduped_16_1, KroneckerMat( HomalgIdentityMatrix( deduped_24_1, deduped_26_1 ), ConvertMatrixToRow( deduped_17_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                  local deduped_1_2;
-                                  deduped_1_2 := (i_2 - 1);
-                                  return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                              end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_26_1 ), deduped_17_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_22_1 * deduped_24_1), deduped_26_1 ), deduped_17_1 ) ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_16_1, ConvertMatrixToRow( deduped_19_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_20_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1;
+    deduped_24_1 := List( list_1, Dimension );
+    deduped_23_1 := UnderlyingRing( cat_1 );
+    deduped_22_1 := deduped_24_1[2];
+    deduped_21_1 := deduped_24_1[1];
+    deduped_20_1 := deduped_24_1[4];
+    deduped_19_1 := deduped_24_1[3];
+    deduped_18_1 := deduped_21_1 * deduped_19_1;
+    deduped_17_1 := HomalgIdentityMatrix( deduped_19_1, deduped_23_1 );
+    deduped_16_1 := deduped_22_1 * deduped_20_1;
+    deduped_15_1 := HomalgIdentityMatrix( deduped_20_1, deduped_23_1 );
+    deduped_14_1 := deduped_19_1 * deduped_20_1;
+    deduped_13_1 := deduped_14_1 * deduped_14_1;
+    deduped_12_1 := deduped_18_1 * deduped_16_1;
+    deduped_11_1 := deduped_19_1 * deduped_16_1;
+    deduped_10_1 := HomalgIdentityMatrix( deduped_12_1, deduped_23_1 );
+    deduped_9_1 := deduped_12_1 * deduped_14_1;
+    hoisted_8_1 := deduped_12_1;
+    hoisted_7_1 := deduped_14_1;
+    hoisted_6_1 := deduped_16_1;
+    hoisted_5_1 := deduped_21_1;
+    hoisted_4_1 := deduped_19_1;
+    hoisted_3_1 := deduped_22_1;
+    hoisted_2_1 := deduped_20_1;
+    morphism_attr_1_1 := DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_14_1, DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_21_1, DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToRow( deduped_15_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                    local deduped_1_2;
+                                    deduped_1_2 := (i_2 - 1);
+                                    return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                                end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_23_1 ), deduped_15_1 ) ) ) * KroneckerMat( KroneckerMat( (DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_21_1, ConvertMatrixToRow( deduped_17_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                                end ) ), deduped_20_1 ), deduped_20_1, deduped_20_1, deduped_26_1 ), deduped_19_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_21_1 * deduped_23_1), deduped_26_1 ), deduped_19_1 )), HomalgIdentityMatrix( deduped_18_1, deduped_26_1 ) ), deduped_17_1 ) * KroneckerMat( KroneckerMat( HomalgIdentityMatrix( deduped_20_1, deduped_26_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
+                                end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_23_1 ), deduped_17_1 )), HomalgIdentityMatrix( deduped_16_1, deduped_23_1 ) ), deduped_15_1 ) * KroneckerMat( DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_18_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
+                            end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_23_1 ) ) ), deduped_15_1 ) ) ) * (DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                        end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_26_1 ) ), deduped_17_1 ) ) * (KroneckerMat( deduped_11_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                      end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_26_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+                            return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
+                        end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_23_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                      end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_26_1 ), deduped_10_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_11_1 ), deduped_10_1 ));
+                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_23_1 ), deduped_10_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_14_1, deduped_23_1 ) ), deduped_10_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -1856,54 +1844,52 @@ end
         
 ########
 function ( cat_1, list_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1, deduped_27_1;
-    deduped_27_1 := UnderlyingRing( cat_1 );
-    deduped_26_1 := List( list_1, Dimension );
-    deduped_25_1 := deduped_26_1[2];
-    deduped_24_1 := deduped_26_1[1];
-    deduped_23_1 := deduped_26_1[4];
-    deduped_22_1 := deduped_26_1[3];
-    deduped_21_1 := HomalgIdentityMatrix( deduped_22_1, deduped_27_1 );
-    deduped_20_1 := HomalgIdentityMatrix( deduped_23_1, deduped_27_1 );
-    deduped_19_1 := HomalgIdentityMatrix( deduped_24_1, deduped_27_1 );
-    deduped_18_1 := deduped_25_1 * deduped_23_1;
-    deduped_17_1 := deduped_24_1 * deduped_22_1;
-    deduped_16_1 := deduped_22_1 * deduped_23_1;
-    deduped_15_1 := deduped_22_1 * deduped_18_1;
-    deduped_14_1 := deduped_16_1 * deduped_16_1;
-    deduped_13_1 := deduped_17_1 * deduped_18_1;
-    deduped_12_1 := HomalgIdentityMatrix( deduped_16_1, deduped_27_1 );
-    deduped_11_1 := HomalgIdentityMatrix( deduped_13_1, deduped_27_1 );
-    deduped_10_1 := deduped_13_1 * deduped_16_1;
-    hoisted_3_1 := deduped_13_1;
-    hoisted_2_1 := deduped_16_1;
-    deduped_9_1 := KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_27_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1;
+    deduped_25_1 := List( list_1, Dimension );
+    deduped_24_1 := UnderlyingRing( cat_1 );
+    deduped_23_1 := deduped_25_1[2];
+    deduped_22_1 := deduped_25_1[1];
+    deduped_21_1 := deduped_25_1[4];
+    deduped_20_1 := deduped_25_1[3];
+    deduped_19_1 := HomalgIdentityMatrix( deduped_20_1, deduped_24_1 );
+    deduped_18_1 := HomalgIdentityMatrix( deduped_21_1, deduped_24_1 );
+    deduped_17_1 := deduped_23_1 * deduped_21_1;
+    deduped_16_1 := deduped_22_1 * deduped_20_1;
+    deduped_15_1 := deduped_20_1 * deduped_21_1;
+    deduped_14_1 := deduped_20_1 * deduped_17_1;
+    deduped_13_1 := deduped_15_1 * deduped_15_1;
+    deduped_12_1 := deduped_16_1 * deduped_17_1;
+    deduped_11_1 := HomalgIdentityMatrix( deduped_12_1, deduped_24_1 );
+    deduped_10_1 := deduped_12_1 * deduped_15_1;
+    hoisted_3_1 := deduped_12_1;
+    hoisted_2_1 := deduped_15_1;
+    deduped_9_1 := DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_24_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_27_1 ), deduped_11_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_12_1 ), deduped_11_1 );
-    hoisted_8_1 := deduped_18_1;
-    hoisted_7_1 := deduped_24_1;
-    hoisted_6_1 := deduped_22_1;
-    hoisted_5_1 := deduped_25_1;
-    hoisted_4_1 := deduped_23_1;
-    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_27_1 ), KroneckerMat( TransposedMatrix( deduped_12_1 ), KroneckerMat( deduped_19_1, KroneckerMat( HomalgIdentityMatrix( deduped_25_1, deduped_27_1 ), ConvertMatrixToRow( deduped_20_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                    local deduped_1_2;
-                                    deduped_1_2 := (i_2 - 1);
-                                    return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                                end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_27_1 ), deduped_20_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_23_1 * deduped_25_1), deduped_27_1 ), deduped_20_1 ) ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_19_1, ConvertMatrixToRow( deduped_21_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                    end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_24_1 ), deduped_11_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_15_1, deduped_24_1 ) ), deduped_11_1 );
+    hoisted_8_1 := deduped_17_1;
+    hoisted_7_1 := deduped_22_1;
+    hoisted_6_1 := deduped_20_1;
+    hoisted_5_1 := deduped_23_1;
+    hoisted_4_1 := deduped_21_1;
+    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_24_1 ), DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_23_1, ConvertMatrixToRow( deduped_18_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                                      local deduped_1_2;
+                                      deduped_1_2 := (i_2 - 1);
+                                      return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                                  end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_24_1 ), deduped_18_1 ) ) ) * KroneckerMat( KroneckerMat( (DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToRow( deduped_19_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
                                       local deduped_1_2;
                                       deduped_1_2 := (i_2 - 1);
                                       return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                                  end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_27_1 ), deduped_21_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_22_1 * deduped_24_1), deduped_27_1 ), deduped_21_1 )), HomalgIdentityMatrix( deduped_18_1, deduped_27_1 ) ), deduped_20_1 ) * KroneckerMat( KroneckerMat( HomalgIdentityMatrix( deduped_17_1, deduped_27_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
-                          end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_27_1 ) ), deduped_20_1 ) ) * deduped_9_1 );
+                                  end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_24_1 ), deduped_19_1 )), HomalgIdentityMatrix( deduped_17_1, deduped_24_1 ) ), deduped_18_1 ) * KroneckerMat( DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_16_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
+                              end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_24_1 ) ) ), deduped_18_1 ) ) ) * deduped_9_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -1915,54 +1901,52 @@ end
         
 ########
 function ( cat_1, source_1, list_1, range_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1, deduped_27_1;
-    deduped_27_1 := UnderlyingRing( cat_1 );
-    deduped_26_1 := List( list_1, Dimension );
-    deduped_25_1 := deduped_26_1[2];
-    deduped_24_1 := deduped_26_1[1];
-    deduped_23_1 := deduped_26_1[4];
-    deduped_22_1 := deduped_26_1[3];
-    deduped_21_1 := HomalgIdentityMatrix( deduped_22_1, deduped_27_1 );
-    deduped_20_1 := HomalgIdentityMatrix( deduped_23_1, deduped_27_1 );
-    deduped_19_1 := HomalgIdentityMatrix( deduped_24_1, deduped_27_1 );
-    deduped_18_1 := deduped_25_1 * deduped_23_1;
-    deduped_17_1 := deduped_24_1 * deduped_22_1;
-    deduped_16_1 := deduped_22_1 * deduped_23_1;
-    deduped_15_1 := deduped_22_1 * deduped_18_1;
-    deduped_14_1 := deduped_16_1 * deduped_16_1;
-    deduped_13_1 := deduped_17_1 * deduped_18_1;
-    deduped_12_1 := HomalgIdentityMatrix( deduped_16_1, deduped_27_1 );
-    deduped_11_1 := HomalgIdentityMatrix( deduped_13_1, deduped_27_1 );
-    deduped_10_1 := deduped_13_1 * deduped_16_1;
-    hoisted_3_1 := deduped_13_1;
-    hoisted_2_1 := deduped_16_1;
-    deduped_9_1 := KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_27_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1;
+    deduped_25_1 := List( list_1, Dimension );
+    deduped_24_1 := UnderlyingRing( cat_1 );
+    deduped_23_1 := deduped_25_1[2];
+    deduped_22_1 := deduped_25_1[1];
+    deduped_21_1 := deduped_25_1[4];
+    deduped_20_1 := deduped_25_1[3];
+    deduped_19_1 := HomalgIdentityMatrix( deduped_20_1, deduped_24_1 );
+    deduped_18_1 := HomalgIdentityMatrix( deduped_21_1, deduped_24_1 );
+    deduped_17_1 := deduped_23_1 * deduped_21_1;
+    deduped_16_1 := deduped_22_1 * deduped_20_1;
+    deduped_15_1 := deduped_20_1 * deduped_21_1;
+    deduped_14_1 := deduped_20_1 * deduped_17_1;
+    deduped_13_1 := deduped_15_1 * deduped_15_1;
+    deduped_12_1 := deduped_16_1 * deduped_17_1;
+    deduped_11_1 := HomalgIdentityMatrix( deduped_12_1, deduped_24_1 );
+    deduped_10_1 := deduped_12_1 * deduped_15_1;
+    hoisted_3_1 := deduped_12_1;
+    hoisted_2_1 := deduped_15_1;
+    deduped_9_1 := DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_24_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_27_1 ), deduped_11_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_12_1 ), deduped_11_1 );
-    hoisted_8_1 := deduped_18_1;
-    hoisted_7_1 := deduped_24_1;
-    hoisted_6_1 := deduped_22_1;
-    hoisted_5_1 := deduped_25_1;
-    hoisted_4_1 := deduped_23_1;
-    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_27_1 ), KroneckerMat( TransposedMatrix( deduped_12_1 ), KroneckerMat( deduped_19_1, KroneckerMat( HomalgIdentityMatrix( deduped_25_1, deduped_27_1 ), ConvertMatrixToRow( deduped_20_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                    local deduped_1_2;
-                                    deduped_1_2 := (i_2 - 1);
-                                    return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                                end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_27_1 ), deduped_20_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_23_1 * deduped_25_1), deduped_27_1 ), deduped_20_1 ) ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_19_1, ConvertMatrixToRow( deduped_21_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                    end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_24_1 ), deduped_11_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_15_1, deduped_24_1 ) ), deduped_11_1 );
+    hoisted_8_1 := deduped_17_1;
+    hoisted_7_1 := deduped_22_1;
+    hoisted_6_1 := deduped_20_1;
+    hoisted_5_1 := deduped_23_1;
+    hoisted_4_1 := deduped_21_1;
+    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_24_1 ), DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_23_1, ConvertMatrixToRow( deduped_18_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                                      local deduped_1_2;
+                                      deduped_1_2 := (i_2 - 1);
+                                      return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                                  end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_24_1 ), deduped_18_1 ) ) ) * KroneckerMat( KroneckerMat( (DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToRow( deduped_19_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
                                       local deduped_1_2;
                                       deduped_1_2 := (i_2 - 1);
                                       return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                                  end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_27_1 ), deduped_21_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_22_1 * deduped_24_1), deduped_27_1 ), deduped_21_1 )), HomalgIdentityMatrix( deduped_18_1, deduped_27_1 ) ), deduped_20_1 ) * KroneckerMat( KroneckerMat( HomalgIdentityMatrix( deduped_17_1, deduped_27_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
-                          end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_27_1 ) ), deduped_20_1 ) ) * deduped_9_1 );
+                                  end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_24_1 ), deduped_19_1 )), HomalgIdentityMatrix( deduped_17_1, deduped_24_1 ) ), deduped_18_1 ) * KroneckerMat( DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_16_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
+                              end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_24_1 ) ) ), deduped_18_1 ) ) ) * deduped_9_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -1974,53 +1958,51 @@ end
         
 ########
 function ( cat_1, source_1, list_1, range_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1;
-    deduped_26_1 := UnderlyingRing( cat_1 );
-    deduped_25_1 := List( list_1, Dimension );
-    deduped_24_1 := deduped_25_1[2];
-    deduped_23_1 := deduped_25_1[1];
-    deduped_22_1 := deduped_25_1[4];
-    deduped_21_1 := deduped_25_1[3];
-    deduped_20_1 := deduped_23_1 * deduped_21_1;
-    deduped_19_1 := HomalgIdentityMatrix( deduped_21_1, deduped_26_1 );
-    deduped_18_1 := deduped_24_1 * deduped_22_1;
-    deduped_17_1 := HomalgIdentityMatrix( deduped_22_1, deduped_26_1 );
-    deduped_16_1 := HomalgIdentityMatrix( deduped_23_1, deduped_26_1 );
-    deduped_15_1 := deduped_21_1 * deduped_22_1;
-    deduped_14_1 := deduped_15_1 * deduped_15_1;
-    deduped_13_1 := deduped_20_1 * deduped_18_1;
-    deduped_12_1 := deduped_21_1 * deduped_18_1;
-    deduped_11_1 := HomalgIdentityMatrix( deduped_15_1, deduped_26_1 );
-    deduped_10_1 := HomalgIdentityMatrix( deduped_13_1, deduped_26_1 );
-    deduped_9_1 := deduped_13_1 * deduped_15_1;
-    hoisted_8_1 := deduped_13_1;
-    hoisted_7_1 := deduped_15_1;
-    hoisted_6_1 := deduped_18_1;
-    hoisted_5_1 := deduped_23_1;
-    hoisted_4_1 := deduped_21_1;
-    hoisted_3_1 := deduped_24_1;
-    hoisted_2_1 := deduped_22_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_11_1 ), KroneckerMat( deduped_16_1, KroneckerMat( HomalgIdentityMatrix( deduped_24_1, deduped_26_1 ), ConvertMatrixToRow( deduped_17_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                  local deduped_1_2;
-                                  deduped_1_2 := (i_2 - 1);
-                                  return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                              end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_26_1 ), deduped_17_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_22_1 * deduped_24_1), deduped_26_1 ), deduped_17_1 ) ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_16_1, ConvertMatrixToRow( deduped_19_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_20_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1;
+    deduped_24_1 := List( list_1, Dimension );
+    deduped_23_1 := UnderlyingRing( cat_1 );
+    deduped_22_1 := deduped_24_1[2];
+    deduped_21_1 := deduped_24_1[1];
+    deduped_20_1 := deduped_24_1[4];
+    deduped_19_1 := deduped_24_1[3];
+    deduped_18_1 := deduped_21_1 * deduped_19_1;
+    deduped_17_1 := HomalgIdentityMatrix( deduped_19_1, deduped_23_1 );
+    deduped_16_1 := deduped_22_1 * deduped_20_1;
+    deduped_15_1 := HomalgIdentityMatrix( deduped_20_1, deduped_23_1 );
+    deduped_14_1 := deduped_19_1 * deduped_20_1;
+    deduped_13_1 := deduped_14_1 * deduped_14_1;
+    deduped_12_1 := deduped_18_1 * deduped_16_1;
+    deduped_11_1 := deduped_19_1 * deduped_16_1;
+    deduped_10_1 := HomalgIdentityMatrix( deduped_12_1, deduped_23_1 );
+    deduped_9_1 := deduped_12_1 * deduped_14_1;
+    hoisted_8_1 := deduped_12_1;
+    hoisted_7_1 := deduped_14_1;
+    hoisted_6_1 := deduped_16_1;
+    hoisted_5_1 := deduped_21_1;
+    hoisted_4_1 := deduped_19_1;
+    hoisted_3_1 := deduped_22_1;
+    hoisted_2_1 := deduped_20_1;
+    morphism_attr_1_1 := DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_14_1, DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_21_1, DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToRow( deduped_15_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                    local deduped_1_2;
+                                    deduped_1_2 := (i_2 - 1);
+                                    return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                                end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_23_1 ), deduped_15_1 ) ) ) * KroneckerMat( KroneckerMat( (DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_21_1, ConvertMatrixToRow( deduped_17_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                                end ) ), deduped_20_1 ), deduped_20_1, deduped_20_1, deduped_26_1 ), deduped_19_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_21_1 * deduped_23_1), deduped_26_1 ), deduped_19_1 )), HomalgIdentityMatrix( deduped_18_1, deduped_26_1 ) ), deduped_17_1 ) * KroneckerMat( KroneckerMat( HomalgIdentityMatrix( deduped_20_1, deduped_26_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
+                                end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_23_1 ), deduped_17_1 )), HomalgIdentityMatrix( deduped_16_1, deduped_23_1 ) ), deduped_15_1 ) * KroneckerMat( DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_18_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
+                            end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_23_1 ) ) ), deduped_15_1 ) ) ) * (DiagMat( deduped_23_1, ListWithIdenticalEntries( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                        end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_26_1 ) ), deduped_17_1 ) ) * (KroneckerMat( deduped_11_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                      end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_26_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+                            return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
+                        end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_23_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                      end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_26_1 ), deduped_10_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_11_1 ), deduped_10_1 ));
+                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_23_1 ), deduped_10_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_14_1, deduped_23_1 ) ), deduped_10_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2034,17 +2016,17 @@ end
 function ( cat_1, a_1, b_1, f_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := UnderlyingRing( cat_1 );
-    deduped_6_1 := Dimension( a_1 );
-    deduped_5_1 := deduped_6_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_7_1 );
-    hoisted_3_1 := deduped_6_1;
+    deduped_7_1 := Dimension( a_1 );
+    deduped_6_1 := UnderlyingRing( cat_1 );
+    deduped_5_1 := deduped_7_1 * deduped_8_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_6_1 );
+    hoisted_3_1 := deduped_7_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_6_1, deduped_7_1 ), ConvertMatrixToRow( deduped_4_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_8_1 * deduped_6_1), deduped_7_1 ), deduped_4_1 ) * KroneckerMat( UnderlyingMatrix( f_1 ), deduped_4_1 );
+    morphism_attr_1_1 := DiagMat( deduped_6_1, ListWithIdenticalEntries( deduped_7_1, ConvertMatrixToRow( deduped_4_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( UnderlyingMatrix( f_1 ), deduped_4_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2101,11 +2083,11 @@ function ( cat_1, b_1, c_1, g_1 )
     deduped_4_1 := HomalgIdentityMatrix( deduped_6_1, deduped_7_1 );
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( UnderlyingMatrix( g_1 ), deduped_4_1 ) * (KroneckerMat( HomalgIdentityMatrix( deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_8_1, deduped_7_1 ), ConvertMatrixToColumn( deduped_4_1 ) ));
+    morphism_attr_1_1 := KroneckerMat( UnderlyingMatrix( g_1 ), deduped_4_1 ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, ConvertMatrixToColumn( deduped_4_1 ) ) ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2783,23 +2765,22 @@ end
         
 ########
 function ( cat_1, a_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := 1 * 1;
-    deduped_7_1 := Dimension( a_1 );
-    deduped_6_1 := UnderlyingRing( cat_1 );
-    deduped_5_1 := deduped_7_1 * 1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_7_1, deduped_6_1 );
-    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
-    hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_3_1 ), deduped_4_1 ) * (KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := 1 * 1;
+    deduped_6_1 := Dimension( a_1 );
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := HomalgIdentityMatrix( deduped_6_1, deduped_5_1 );
+    deduped_3_1 := deduped_6_1 * 1;
+    hoisted_2_1 := deduped_6_1;
+    morphism_attr_1_1 := DiagMat( deduped_5_1, ListWithIdenticalEntries( 1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_3_1 ), deduped_4_1 ));
+                      end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_5_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_5_1 ), deduped_4_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( 1, deduped_5_1 ) ), deduped_4_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2811,23 +2792,22 @@ end
         
 ########
 function ( cat_1, a_1, s_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := 1 * 1;
-    deduped_7_1 := Dimension( a_1 );
-    deduped_6_1 := UnderlyingRing( cat_1 );
-    deduped_5_1 := deduped_7_1 * 1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_7_1, deduped_6_1 );
-    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
-    hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_3_1 ), deduped_4_1 ) * (KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := 1 * 1;
+    deduped_6_1 := Dimension( a_1 );
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := HomalgIdentityMatrix( deduped_6_1, deduped_5_1 );
+    deduped_3_1 := deduped_6_1 * 1;
+    hoisted_2_1 := deduped_6_1;
+    morphism_attr_1_1 := DiagMat( deduped_5_1, ListWithIdenticalEntries( 1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_3_1 ), deduped_4_1 ));
+                      end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_5_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_5_1 ), deduped_4_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( 1, deduped_5_1 ) ), deduped_4_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2869,11 +2849,11 @@ function ( cat_1, a_1 )
     deduped_4_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
     deduped_3_1 := 1 * deduped_5_1;
     hoisted_2_1 := deduped_5_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_3_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_5_1, deduped_6_1 ), ConvertMatrixToColumn( deduped_4_1 ) );
+    morphism_attr_1_1 := KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                  end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_6_1 ), deduped_4_1 ) * DiagMat( deduped_6_1, ListWithIdenticalEntries( deduped_5_1, ConvertMatrixToColumn( deduped_4_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2891,11 +2871,11 @@ function ( cat_1, a_1, s_1 )
     deduped_4_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
     deduped_3_1 := 1 * deduped_5_1;
     hoisted_2_1 := deduped_5_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_3_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_5_1, deduped_6_1 ), ConvertMatrixToColumn( deduped_4_1 ) );
+    morphism_attr_1_1 := KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                  end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_6_1 ), deduped_4_1 ) * DiagMat( deduped_6_1, ListWithIdenticalEntries( deduped_5_1, ConvertMatrixToColumn( deduped_4_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2977,16 +2957,16 @@ end
 ########
 function ( cat_1, a_1 )
     local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1;
-    deduped_6_1 := UnderlyingRing( cat_1 );
-    deduped_5_1 := Dimension( a_1 );
-    deduped_4_1 := deduped_5_1 * 1;
-    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
-    hoisted_2_1 := deduped_5_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_5_1, deduped_6_1 ), ConvertMatrixToRow( deduped_3_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                    end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_6_1 ), deduped_3_1 ) * KroneckerMat( HomalgIdentityMatrix( (1 * deduped_5_1), deduped_6_1 ), deduped_3_1 );
+    deduped_6_1 := Dimension( a_1 );
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := deduped_6_1 * 1;
+    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_5_1 );
+    hoisted_2_1 := deduped_6_1;
+    morphism_attr_1_1 := DiagMat( deduped_5_1, ListWithIdenticalEntries( deduped_6_1, ConvertMatrixToRow( deduped_3_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                  end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_5_1 ), deduped_3_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), a_1, UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -2999,16 +2979,16 @@ end
 ########
 function ( cat_1, a_1, r_1 )
     local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1;
-    deduped_6_1 := UnderlyingRing( cat_1 );
-    deduped_5_1 := Dimension( a_1 );
-    deduped_4_1 := deduped_5_1 * 1;
-    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
-    hoisted_2_1 := deduped_5_1;
-    morphism_attr_1_1 := KroneckerMat( HomalgIdentityMatrix( deduped_5_1, deduped_6_1 ), ConvertMatrixToRow( deduped_3_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                    end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_6_1 ), deduped_3_1 ) * KroneckerMat( HomalgIdentityMatrix( (1 * deduped_5_1), deduped_6_1 ), deduped_3_1 );
+    deduped_6_1 := Dimension( a_1 );
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := deduped_6_1 * 1;
+    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_5_1 );
+    hoisted_2_1 := deduped_6_1;
+    morphism_attr_1_1 := DiagMat( deduped_5_1, ListWithIdenticalEntries( deduped_6_1, ConvertMatrixToRow( deduped_3_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                      local deduped_1_2;
+                      deduped_1_2 := (i_2 - 1);
+                      return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                  end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_5_1 ), deduped_3_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), r_1, UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3020,23 +3000,22 @@ end
         
 ########
 function ( cat_1, a_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := 1 * 1;
-    deduped_7_1 := Dimension( a_1 );
-    deduped_6_1 := UnderlyingRing( cat_1 );
-    deduped_5_1 := 1 * deduped_7_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_7_1, deduped_6_1 );
-    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
-    hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_3_1 ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := 1 * 1;
+    deduped_6_1 := Dimension( a_1 );
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := 1 * deduped_6_1;
+    deduped_3_1 := HomalgIdentityMatrix( deduped_6_1, deduped_5_1 );
+    hoisted_2_1 := deduped_6_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( 1, deduped_5_1 ) ), deduped_3_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_5_1 ), deduped_3_1 ) * DiagMat( deduped_5_1, ListWithIdenticalEntries( 1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ) ) * KroneckerMat( TransposedMatrix( deduped_3_1 ), deduped_4_1 );
+                    end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_5_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3048,23 +3027,22 @@ end
         
 ########
 function ( cat_1, a_1, r_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := 1 * 1;
-    deduped_7_1 := Dimension( a_1 );
-    deduped_6_1 := UnderlyingRing( cat_1 );
-    deduped_5_1 := 1 * deduped_7_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_7_1, deduped_6_1 );
-    deduped_3_1 := HomalgIdentityMatrix( 1, deduped_6_1 );
-    hoisted_2_1 := deduped_7_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_3_1 ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_6_1 ), deduped_4_1 ) * KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := 1 * 1;
+    deduped_6_1 := Dimension( a_1 );
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := 1 * deduped_6_1;
+    deduped_3_1 := HomalgIdentityMatrix( deduped_6_1, deduped_5_1 );
+    hoisted_2_1 := deduped_6_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( 1, deduped_5_1 ) ), deduped_3_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, 1 ) * 1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_5_1 ), deduped_3_1 ) * DiagMat( deduped_5_1, ListWithIdenticalEntries( 1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
                         local deduped_1_2;
                         deduped_1_2 := (i_2 - 1);
                         return (REM_INT( deduped_1_2, hoisted_2_1 ) * 1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_6_1 ) ) * KroneckerMat( TransposedMatrix( deduped_3_1 ), deduped_4_1 );
+                    end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_5_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3269,11 +3247,11 @@ function ( cat_1, a_1, b_1, alpha_1 )
     deduped_4_1 := HomalgIdentityMatrix( deduped_6_1, deduped_7_1 );
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( UnderlyingMatrix( alpha_1 ), deduped_4_1 ) * (KroneckerMat( HomalgIdentityMatrix( deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_8_1, deduped_7_1 ), ConvertMatrixToColumn( deduped_4_1 ) ));
+    morphism_attr_1_1 := KroneckerMat( UnderlyingMatrix( alpha_1 ), deduped_4_1 ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                        local deduped_1_2;
+                        deduped_1_2 := (i_2 - 1);
+                        return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_4_1 ) * DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, ConvertMatrixToColumn( deduped_4_1 ) ) ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3285,23 +3263,22 @@ end
         
 ########
 function ( cat_1, alpha_1 )
-    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1;
-    deduped_8_1 := UnderlyingRing( cat_1 );
-    deduped_7_1 := HomalgIdentityMatrix( 1, deduped_8_1 );
-    deduped_6_1 := Dimension( Source( alpha_1 ) );
-    deduped_5_1 := deduped_6_1 * 1;
-    deduped_4_1 := deduped_6_1 * deduped_6_1;
-    deduped_3_1 := HomalgIdentityMatrix( deduped_6_1, deduped_8_1 );
-    hoisted_2_1 := deduped_6_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_3_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( 1, deduped_7_1 );
+    deduped_5_1 := Dimension( Source( alpha_1 ) );
+    deduped_4_1 := deduped_5_1 * 1;
+    deduped_3_1 := deduped_5_1 * deduped_5_1;
+    hoisted_2_1 := deduped_5_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_5_1, deduped_7_1 ) ), deduped_6_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_7_1 ) * KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                    end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ) ) * KroneckerMat( TransposedMatrix( deduped_3_1 ), UnderlyingMatrix( alpha_1 ) );
+                      end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, deduped_7_1 ), deduped_6_1 ) * DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_5_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                      end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ) ) ) * DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_5_1, UnderlyingMatrix( alpha_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3318,14 +3295,14 @@ function ( cat_1, a_1, L_1 )
     deduped_8_1 := List( L_1, Dimension );
     deduped_7_1 := Dimension( a_1 );
     deduped_6_1 := UnderlyingRing( cat_1 );
-    hoisted_5_1 := HomalgIdentityMatrix( deduped_7_1, deduped_6_1 );
+    hoisted_5_1 := deduped_7_1;
     hoisted_4_1 := deduped_9_1;
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := deduped_8_1;
     morphism_attr_1_1 := UnionOfColumns( deduped_6_1, deduped_7_1 * Sum( deduped_8_1 ), List( [ 1 .. deduped_9_1 ], function ( logic_new_func_x_2 )
               local deduped_1_2;
               deduped_1_2 := hoisted_2_1[logic_new_func_x_2];
-              return KroneckerMat( hoisted_5_1, UnionOfRows( HomalgZeroMatrix( Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), deduped_1_2, hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), deduped_1_2, hoisted_3_1 ) ) );
+              return DiagMat( hoisted_3_1, ListWithIdenticalEntries( hoisted_5_1, UnionOfRows( HomalgZeroMatrix( Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), deduped_1_2, hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), deduped_1_2, hoisted_3_1 ) ) ) );
           end ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
@@ -3341,14 +3318,14 @@ function ( cat_1, s_1, a_1, L_1, r_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1;
     deduped_7_1 := Length( L_1 );
     deduped_6_1 := UnderlyingRing( cat_1 );
-    hoisted_5_1 := HomalgIdentityMatrix( Dimension( a_1 ), deduped_6_1 );
+    hoisted_5_1 := Dimension( a_1 );
     hoisted_4_1 := deduped_7_1;
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := List( L_1, Dimension );
     morphism_attr_1_1 := UnionOfColumns( deduped_6_1, Dimension( s_1 ), List( [ 1 .. deduped_7_1 ], function ( logic_new_func_x_2 )
               local deduped_1_2;
               deduped_1_2 := hoisted_2_1[logic_new_func_x_2];
-              return KroneckerMat( hoisted_5_1, UnionOfRows( HomalgZeroMatrix( Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), deduped_1_2, hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), deduped_1_2, hoisted_3_1 ) ) );
+              return DiagMat( hoisted_3_1, ListWithIdenticalEntries( hoisted_5_1, UnionOfRows( HomalgZeroMatrix( Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), deduped_1_2, hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), deduped_1_2, hoisted_3_1 ) ) ) );
           end ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
@@ -3366,14 +3343,14 @@ function ( cat_1, a_1, L_1 )
     deduped_8_1 := List( L_1, Dimension );
     deduped_7_1 := Dimension( a_1 );
     deduped_6_1 := UnderlyingRing( cat_1 );
-    hoisted_5_1 := HomalgIdentityMatrix( deduped_7_1, deduped_6_1 );
+    hoisted_5_1 := deduped_7_1;
     hoisted_4_1 := deduped_9_1;
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := deduped_8_1;
     morphism_attr_1_1 := UnionOfRows( deduped_6_1, deduped_7_1 * Sum( deduped_8_1 ), List( [ 1 .. deduped_9_1 ], function ( logic_new_func_x_2 )
               local deduped_1_2;
               deduped_1_2 := hoisted_2_1[logic_new_func_x_2];
-              return KroneckerMat( hoisted_5_1, UnionOfColumns( HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), hoisted_3_1 ) ) );
+              return DiagMat( hoisted_3_1, ListWithIdenticalEntries( hoisted_5_1, UnionOfColumns( HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), hoisted_3_1 ) ) ) );
           end ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
@@ -3389,14 +3366,14 @@ function ( cat_1, s_1, a_1, L_1, r_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1;
     deduped_7_1 := Length( L_1 );
     deduped_6_1 := UnderlyingRing( cat_1 );
-    hoisted_5_1 := HomalgIdentityMatrix( Dimension( a_1 ), deduped_6_1 );
+    hoisted_5_1 := Dimension( a_1 );
     hoisted_4_1 := deduped_7_1;
     hoisted_3_1 := deduped_6_1;
     hoisted_2_1 := List( L_1, Dimension );
     morphism_attr_1_1 := UnionOfRows( deduped_6_1, Dimension( r_1 ), List( [ 1 .. deduped_7_1 ], function ( logic_new_func_x_2 )
               local deduped_1_2;
               deduped_1_2 := hoisted_2_1[logic_new_func_x_2];
-              return KroneckerMat( hoisted_5_1, UnionOfColumns( HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), hoisted_3_1 ) ) );
+              return DiagMat( hoisted_3_1, ListWithIdenticalEntries( hoisted_5_1, UnionOfColumns( HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ 1 .. logic_new_func_x_2 - 1 ]} ), hoisted_3_1 ), HomalgIdentityMatrix( deduped_1_2, hoisted_3_1 ), HomalgZeroMatrix( deduped_1_2, Sum( hoisted_2_1{[ logic_new_func_x_2 + 1 .. hoisted_4_1 ]} ), hoisted_3_1 ) ) ) );
           end ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), r_1, UnderlyingMatrix, morphism_attr_1_1 );
 end
@@ -3505,37 +3482,37 @@ function ( cat_1, a_1, b_1, c_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1;
     deduped_17_1 := Dimension( b_1 );
     deduped_16_1 := Dimension( a_1 );
-    deduped_15_1 := UnderlyingRing( cat_1 );
-    deduped_14_1 := Dimension( c_1 );
-    deduped_13_1 := deduped_14_1 * deduped_14_1;
-    deduped_12_1 := deduped_17_1 * deduped_14_1;
-    deduped_11_1 := deduped_16_1 * deduped_17_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_17_1, deduped_15_1 );
-    deduped_9_1 := HomalgIdentityMatrix( deduped_14_1, deduped_15_1 );
-    deduped_8_1 := deduped_11_1 * deduped_12_1;
-    deduped_7_1 := HomalgIdentityMatrix( deduped_8_1, deduped_15_1 );
-    deduped_6_1 := deduped_8_1 * deduped_14_1;
+    deduped_15_1 := Dimension( c_1 );
+    deduped_14_1 := UnderlyingRing( cat_1 );
+    deduped_13_1 := deduped_15_1 * deduped_15_1;
+    deduped_12_1 := deduped_17_1 * deduped_15_1;
+    deduped_11_1 := HomalgIdentityMatrix( deduped_15_1, deduped_14_1 );
+    deduped_10_1 := deduped_16_1 * deduped_17_1;
+    deduped_9_1 := HomalgIdentityMatrix( deduped_17_1, deduped_14_1 );
+    deduped_8_1 := deduped_10_1 * deduped_12_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_8_1, deduped_14_1 );
+    deduped_6_1 := deduped_8_1 * deduped_15_1;
     hoisted_5_1 := deduped_8_1;
-    hoisted_4_1 := deduped_14_1;
+    hoisted_4_1 := deduped_15_1;
     hoisted_3_1 := deduped_16_1;
     hoisted_2_1 := deduped_17_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_9_1 ), KroneckerMat( HomalgIdentityMatrix( deduped_16_1, deduped_15_1 ), ConvertMatrixToRow( deduped_10_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_15_1, DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_16_1, ConvertMatrixToRow( deduped_9_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
                               local deduped_1_2;
                               deduped_1_2 := (i_2 - 1);
                               return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                          end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_15_1 ), deduped_10_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_17_1 * deduped_16_1), deduped_15_1 ), deduped_10_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_11_1, deduped_15_1 ), (KroneckerMat( deduped_10_1, ConvertMatrixToRow( deduped_9_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                            end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_15_1 ), deduped_9_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_14_1 * deduped_17_1), deduped_15_1 ), deduped_9_1 )) ) ) * (KroneckerMat( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_15_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_14_1 ), deduped_9_1 ) * DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_10_1, (DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_17_1, ConvertMatrixToRow( deduped_11_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_14_1 ), deduped_11_1 )) ) ) ) ) * (DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_14_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_15_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_9_1 ), deduped_7_1 ));
+                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_14_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_11_1 ), deduped_7_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3550,37 +3527,37 @@ function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1;
     deduped_17_1 := Dimension( b_1 );
     deduped_16_1 := Dimension( a_1 );
-    deduped_15_1 := UnderlyingRing( cat_1 );
-    deduped_14_1 := Dimension( c_1 );
-    deduped_13_1 := deduped_14_1 * deduped_14_1;
-    deduped_12_1 := deduped_17_1 * deduped_14_1;
-    deduped_11_1 := deduped_16_1 * deduped_17_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_17_1, deduped_15_1 );
-    deduped_9_1 := HomalgIdentityMatrix( deduped_14_1, deduped_15_1 );
-    deduped_8_1 := deduped_11_1 * deduped_12_1;
-    deduped_7_1 := HomalgIdentityMatrix( deduped_8_1, deduped_15_1 );
-    deduped_6_1 := deduped_8_1 * deduped_14_1;
+    deduped_15_1 := Dimension( c_1 );
+    deduped_14_1 := UnderlyingRing( cat_1 );
+    deduped_13_1 := deduped_15_1 * deduped_15_1;
+    deduped_12_1 := deduped_17_1 * deduped_15_1;
+    deduped_11_1 := HomalgIdentityMatrix( deduped_15_1, deduped_14_1 );
+    deduped_10_1 := deduped_16_1 * deduped_17_1;
+    deduped_9_1 := HomalgIdentityMatrix( deduped_17_1, deduped_14_1 );
+    deduped_8_1 := deduped_10_1 * deduped_12_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_8_1, deduped_14_1 );
+    deduped_6_1 := deduped_8_1 * deduped_15_1;
     hoisted_5_1 := deduped_8_1;
-    hoisted_4_1 := deduped_14_1;
+    hoisted_4_1 := deduped_15_1;
     hoisted_3_1 := deduped_16_1;
     hoisted_2_1 := deduped_17_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_9_1 ), KroneckerMat( HomalgIdentityMatrix( deduped_16_1, deduped_15_1 ), ConvertMatrixToRow( deduped_10_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_15_1, DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_16_1, ConvertMatrixToRow( deduped_9_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
                               local deduped_1_2;
                               deduped_1_2 := (i_2 - 1);
                               return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                          end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_15_1 ), deduped_10_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_17_1 * deduped_16_1), deduped_15_1 ), deduped_10_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_11_1, deduped_15_1 ), (KroneckerMat( deduped_10_1, ConvertMatrixToRow( deduped_9_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                            end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_15_1 ), deduped_9_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_14_1 * deduped_17_1), deduped_15_1 ), deduped_9_1 )) ) ) * (KroneckerMat( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_15_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_14_1 ), deduped_9_1 ) * DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_10_1, (DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_17_1, ConvertMatrixToRow( deduped_11_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_14_1 ), deduped_11_1 )) ) ) ) ) * (DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_14_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_15_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_9_1 ), deduped_7_1 ));
+                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_14_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_11_1 ), deduped_7_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3592,41 +3569,40 @@ end
         
 ########
 function ( cat_1, a_1, b_1, c_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1;
-    deduped_18_1 := Dimension( c_1 );
-    deduped_17_1 := Dimension( b_1 );
-    deduped_16_1 := UnderlyingRing( cat_1 );
-    deduped_15_1 := Dimension( a_1 );
-    deduped_14_1 := HomalgIdentityMatrix( deduped_17_1, deduped_16_1 );
-    deduped_13_1 := deduped_15_1 * deduped_15_1;
-    deduped_12_1 := deduped_15_1 * deduped_17_1;
-    deduped_11_1 := deduped_17_1 * deduped_18_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_15_1, deduped_16_1 );
-    deduped_9_1 := HomalgIdentityMatrix( deduped_11_1, deduped_16_1 );
-    deduped_8_1 := deduped_11_1 * deduped_12_1;
-    deduped_7_1 := deduped_15_1 * deduped_8_1;
-    deduped_6_1 := HomalgIdentityMatrix( deduped_8_1, deduped_16_1 );
-    hoisted_5_1 := deduped_18_1;
-    hoisted_4_1 := deduped_17_1;
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1;
+    deduped_17_1 := Dimension( c_1 );
+    deduped_16_1 := Dimension( b_1 );
+    deduped_15_1 := UnderlyingRing( cat_1 );
+    deduped_14_1 := Dimension( a_1 );
+    deduped_13_1 := HomalgIdentityMatrix( deduped_16_1, deduped_15_1 );
+    deduped_12_1 := deduped_14_1 * deduped_14_1;
+    deduped_11_1 := deduped_14_1 * deduped_16_1;
+    deduped_10_1 := deduped_16_1 * deduped_17_1;
+    deduped_9_1 := HomalgIdentityMatrix( deduped_14_1, deduped_15_1 );
+    deduped_8_1 := deduped_10_1 * deduped_11_1;
+    deduped_7_1 := deduped_14_1 * deduped_8_1;
+    deduped_6_1 := HomalgIdentityMatrix( deduped_8_1, deduped_15_1 );
+    hoisted_5_1 := deduped_17_1;
+    hoisted_4_1 := deduped_16_1;
     hoisted_3_1 := deduped_8_1;
-    hoisted_2_1 := deduped_15_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_10_1 ), deduped_6_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+    hoisted_2_1 := deduped_14_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_9_1 ), deduped_6_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_16_1 ), deduped_6_1 ) * KroneckerMat( deduped_10_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_16_1 ) ) * KroneckerMat( TransposedMatrix( deduped_10_1 ), (KroneckerMat( deduped_9_1, KroneckerMat( HomalgIdentityMatrix( deduped_12_1, deduped_16_1 ), deduped_10_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                            end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_16_1 ), deduped_10_1 ) * KroneckerMat( deduped_14_1, ConvertMatrixToColumn( deduped_10_1 ) ) ) * (KroneckerMat( deduped_9_1, deduped_14_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                      end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_15_1 ), deduped_6_1 ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_15_1 ) ) ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_14_1, (DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_10_1, KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_15_1 ), deduped_9_1 ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_16_1, ConvertMatrixToColumn( deduped_9_1 ) ) ) ) ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
                               local deduped_1_2;
                               deduped_1_2 := (i_2 - 1);
                               return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                          end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_16_1 ), deduped_14_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_18_1, deduped_16_1 ), ConvertMatrixToColumn( deduped_14_1 ) ))) );
+                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_15_1 ), deduped_13_1 ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_17_1, ConvertMatrixToColumn( deduped_13_1 ) ) ))) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3638,41 +3614,40 @@ end
         
 ########
 function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1;
-    deduped_18_1 := Dimension( c_1 );
-    deduped_17_1 := Dimension( b_1 );
-    deduped_16_1 := UnderlyingRing( cat_1 );
-    deduped_15_1 := Dimension( a_1 );
-    deduped_14_1 := HomalgIdentityMatrix( deduped_17_1, deduped_16_1 );
-    deduped_13_1 := deduped_15_1 * deduped_15_1;
-    deduped_12_1 := deduped_15_1 * deduped_17_1;
-    deduped_11_1 := deduped_17_1 * deduped_18_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_15_1, deduped_16_1 );
-    deduped_9_1 := HomalgIdentityMatrix( deduped_11_1, deduped_16_1 );
-    deduped_8_1 := deduped_11_1 * deduped_12_1;
-    deduped_7_1 := deduped_15_1 * deduped_8_1;
-    deduped_6_1 := HomalgIdentityMatrix( deduped_8_1, deduped_16_1 );
-    hoisted_5_1 := deduped_18_1;
-    hoisted_4_1 := deduped_17_1;
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1;
+    deduped_17_1 := Dimension( c_1 );
+    deduped_16_1 := Dimension( b_1 );
+    deduped_15_1 := UnderlyingRing( cat_1 );
+    deduped_14_1 := Dimension( a_1 );
+    deduped_13_1 := HomalgIdentityMatrix( deduped_16_1, deduped_15_1 );
+    deduped_12_1 := deduped_14_1 * deduped_14_1;
+    deduped_11_1 := deduped_14_1 * deduped_16_1;
+    deduped_10_1 := deduped_16_1 * deduped_17_1;
+    deduped_9_1 := HomalgIdentityMatrix( deduped_14_1, deduped_15_1 );
+    deduped_8_1 := deduped_10_1 * deduped_11_1;
+    deduped_7_1 := deduped_14_1 * deduped_8_1;
+    deduped_6_1 := HomalgIdentityMatrix( deduped_8_1, deduped_15_1 );
+    hoisted_5_1 := deduped_17_1;
+    hoisted_4_1 := deduped_16_1;
     hoisted_3_1 := deduped_8_1;
-    hoisted_2_1 := deduped_15_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_10_1 ), deduped_6_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+    hoisted_2_1 := deduped_14_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_9_1 ), deduped_6_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_16_1 ), deduped_6_1 ) * KroneckerMat( deduped_10_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_16_1 ) ) * KroneckerMat( TransposedMatrix( deduped_10_1 ), (KroneckerMat( deduped_9_1, KroneckerMat( HomalgIdentityMatrix( deduped_12_1, deduped_16_1 ), deduped_10_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                            end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_16_1 ), deduped_10_1 ) * KroneckerMat( deduped_14_1, ConvertMatrixToColumn( deduped_10_1 ) ) ) * (KroneckerMat( deduped_9_1, deduped_14_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                      end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_15_1 ), deduped_6_1 ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_15_1 ) ) ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_14_1, (DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_10_1, KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_15_1 ), deduped_9_1 ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_16_1, ConvertMatrixToColumn( deduped_9_1 ) ) ) ) ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
                               local deduped_1_2;
                               deduped_1_2 := (i_2 - 1);
                               return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                          end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_16_1 ), deduped_14_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_18_1, deduped_16_1 ), ConvertMatrixToColumn( deduped_14_1 ) ))) );
+                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_15_1 ), deduped_13_1 ) * DiagMat( deduped_15_1, ListWithIdenticalEntries( deduped_17_1, ConvertMatrixToColumn( deduped_13_1 ) ) ))) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3687,48 +3662,48 @@ function ( cat_1, a_1, b_1, c_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1;
     deduped_20_1 := Dimension( b_1 );
     deduped_19_1 := Dimension( a_1 );
-    deduped_18_1 := UnderlyingRing( cat_1 );
-    deduped_17_1 := Dimension( c_1 );
-    deduped_16_1 := deduped_17_1 * deduped_17_1;
-    deduped_15_1 := deduped_20_1 * deduped_17_1;
-    deduped_14_1 := deduped_19_1 * deduped_20_1;
-    deduped_13_1 := HomalgIdentityMatrix( deduped_20_1, deduped_18_1 );
-    deduped_12_1 := HomalgIdentityMatrix( deduped_17_1, deduped_18_1 );
-    deduped_11_1 := deduped_15_1 * deduped_14_1;
-    deduped_10_1 := deduped_17_1 * deduped_14_1;
-    deduped_9_1 := deduped_14_1 * deduped_20_1;
-    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_18_1 );
-    deduped_7_1 := deduped_11_1 * deduped_17_1;
+    deduped_18_1 := Dimension( c_1 );
+    deduped_17_1 := UnderlyingRing( cat_1 );
+    deduped_16_1 := deduped_18_1 * deduped_18_1;
+    deduped_15_1 := deduped_20_1 * deduped_18_1;
+    deduped_14_1 := HomalgIdentityMatrix( deduped_18_1, deduped_17_1 );
+    deduped_13_1 := deduped_19_1 * deduped_20_1;
+    deduped_12_1 := HomalgIdentityMatrix( deduped_20_1, deduped_17_1 );
+    deduped_11_1 := deduped_15_1 * deduped_13_1;
+    deduped_10_1 := deduped_18_1 * deduped_13_1;
+    deduped_9_1 := deduped_13_1 * deduped_20_1;
+    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_17_1 );
+    deduped_7_1 := deduped_11_1 * deduped_18_1;
     hoisted_6_1 := deduped_11_1;
-    hoisted_5_1 := deduped_17_1;
-    hoisted_4_1 := deduped_14_1;
+    hoisted_5_1 := deduped_18_1;
+    hoisted_4_1 := deduped_13_1;
     hoisted_3_1 := deduped_19_1;
     hoisted_2_1 := deduped_20_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_12_1 ), KroneckerMat( HomalgIdentityMatrix( deduped_19_1, deduped_18_1 ), ConvertMatrixToRow( deduped_13_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_18_1, DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_19_1, ConvertMatrixToRow( deduped_12_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                              end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_18_1 ), deduped_13_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_20_1 * deduped_19_1), deduped_18_1 ), deduped_13_1 ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_18_1 ) * KroneckerMat( (KroneckerMat( deduped_13_1, ConvertMatrixToRow( deduped_12_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
+                              end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_17_1 ), deduped_12_1 ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
+                              local deduped_1_2;
+                              deduped_1_2 := (i_2 - 1);
+                              return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                          end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_17_1 ) * KroneckerMat( (DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_20_1, ConvertMatrixToRow( deduped_14_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                              end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_18_1 ), deduped_12_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_17_1 * deduped_20_1), deduped_18_1 ), deduped_12_1 )), HomalgIdentityMatrix( deduped_14_1, deduped_18_1 ) ) * KroneckerMat( HomalgIdentityMatrix( deduped_15_1, deduped_18_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_18_1 ) ) ) * (KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                      end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_18_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                              end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_17_1 ), deduped_14_1 )), HomalgIdentityMatrix( deduped_13_1, deduped_17_1 ) ) * DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                              local deduped_1_2;
+                              deduped_1_2 := (i_2 - 1);
+                              return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_17_1 ) ) ) ) ) * (DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_18_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_17_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                      end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_18_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_12_1 ), deduped_8_1 ));
+                      end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_17_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_14_1 ), deduped_8_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3743,48 +3718,48 @@ function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
     local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1;
     deduped_20_1 := Dimension( b_1 );
     deduped_19_1 := Dimension( a_1 );
-    deduped_18_1 := UnderlyingRing( cat_1 );
-    deduped_17_1 := Dimension( c_1 );
-    deduped_16_1 := deduped_17_1 * deduped_17_1;
-    deduped_15_1 := deduped_20_1 * deduped_17_1;
-    deduped_14_1 := deduped_19_1 * deduped_20_1;
-    deduped_13_1 := HomalgIdentityMatrix( deduped_20_1, deduped_18_1 );
-    deduped_12_1 := HomalgIdentityMatrix( deduped_17_1, deduped_18_1 );
-    deduped_11_1 := deduped_15_1 * deduped_14_1;
-    deduped_10_1 := deduped_17_1 * deduped_14_1;
-    deduped_9_1 := deduped_14_1 * deduped_20_1;
-    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_18_1 );
-    deduped_7_1 := deduped_11_1 * deduped_17_1;
+    deduped_18_1 := Dimension( c_1 );
+    deduped_17_1 := UnderlyingRing( cat_1 );
+    deduped_16_1 := deduped_18_1 * deduped_18_1;
+    deduped_15_1 := deduped_20_1 * deduped_18_1;
+    deduped_14_1 := HomalgIdentityMatrix( deduped_18_1, deduped_17_1 );
+    deduped_13_1 := deduped_19_1 * deduped_20_1;
+    deduped_12_1 := HomalgIdentityMatrix( deduped_20_1, deduped_17_1 );
+    deduped_11_1 := deduped_15_1 * deduped_13_1;
+    deduped_10_1 := deduped_18_1 * deduped_13_1;
+    deduped_9_1 := deduped_13_1 * deduped_20_1;
+    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_17_1 );
+    deduped_7_1 := deduped_11_1 * deduped_18_1;
     hoisted_6_1 := deduped_11_1;
-    hoisted_5_1 := deduped_17_1;
-    hoisted_4_1 := deduped_14_1;
+    hoisted_5_1 := deduped_18_1;
+    hoisted_4_1 := deduped_13_1;
     hoisted_3_1 := deduped_19_1;
     hoisted_2_1 := deduped_20_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_12_1 ), KroneckerMat( HomalgIdentityMatrix( deduped_19_1, deduped_18_1 ), ConvertMatrixToRow( deduped_13_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_18_1, DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_19_1, ConvertMatrixToRow( deduped_12_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                              end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_18_1 ), deduped_13_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_20_1 * deduped_19_1), deduped_18_1 ), deduped_13_1 ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_18_1 ) * KroneckerMat( (KroneckerMat( deduped_13_1, ConvertMatrixToRow( deduped_12_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
+                              end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_17_1 ), deduped_12_1 ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_9_1 ], function ( i_2 )
+                              local deduped_1_2;
+                              deduped_1_2 := (i_2 - 1);
+                              return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                          end ) ), deduped_9_1 ), deduped_9_1, deduped_9_1, deduped_17_1 ) * KroneckerMat( (DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_20_1, ConvertMatrixToRow( deduped_14_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                              end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_18_1 ), deduped_12_1 ) * KroneckerMat( HomalgIdentityMatrix( (deduped_17_1 * deduped_20_1), deduped_18_1 ), deduped_12_1 )), HomalgIdentityMatrix( deduped_14_1, deduped_18_1 ) ) * KroneckerMat( HomalgIdentityMatrix( deduped_15_1, deduped_18_1 ), HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_18_1 ) ) ) * (KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                      end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_18_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                              end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_17_1 ), deduped_14_1 )), HomalgIdentityMatrix( deduped_13_1, deduped_17_1 ) ) * DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                              local deduped_1_2;
+                              deduped_1_2 := (i_2 - 1);
+                              return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                          end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_17_1 ) ) ) ) ) * (DiagMat( deduped_17_1, ListWithIdenticalEntries( deduped_18_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_17_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                      end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_18_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_12_1 ), deduped_8_1 ));
+                      end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_17_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_14_1 ), deduped_8_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3796,53 +3771,51 @@ end
         
 ########
 function ( cat_1, a_1, b_1, c_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1;
-    deduped_22_1 := Dimension( c_1 );
-    deduped_21_1 := Dimension( b_1 );
-    deduped_20_1 := UnderlyingRing( cat_1 );
-    deduped_19_1 := Dimension( a_1 );
-    deduped_18_1 := HomalgIdentityMatrix( deduped_21_1, deduped_20_1 );
-    deduped_17_1 := deduped_19_1 * deduped_19_1;
-    deduped_16_1 := deduped_21_1 * deduped_22_1;
-    deduped_15_1 := deduped_19_1 * deduped_21_1;
-    deduped_14_1 := HomalgIdentityMatrix( deduped_19_1, deduped_20_1 );
-    deduped_13_1 := deduped_21_1 * deduped_16_1;
-    deduped_12_1 := HomalgIdentityMatrix( deduped_16_1, deduped_20_1 );
-    deduped_11_1 := deduped_16_1 * deduped_19_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_15_1, deduped_20_1 );
-    deduped_9_1 := deduped_15_1 * deduped_16_1;
-    deduped_8_1 := deduped_19_1 * deduped_9_1;
-    deduped_7_1 := HomalgIdentityMatrix( deduped_9_1, deduped_20_1 );
-    hoisted_6_1 := deduped_22_1;
-    hoisted_5_1 := deduped_21_1;
-    hoisted_4_1 := deduped_16_1;
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1;
+    deduped_20_1 := Dimension( c_1 );
+    deduped_19_1 := Dimension( b_1 );
+    deduped_18_1 := UnderlyingRing( cat_1 );
+    deduped_17_1 := Dimension( a_1 );
+    deduped_16_1 := HomalgIdentityMatrix( deduped_19_1, deduped_18_1 );
+    deduped_15_1 := deduped_17_1 * deduped_17_1;
+    deduped_14_1 := deduped_19_1 * deduped_20_1;
+    deduped_13_1 := deduped_17_1 * deduped_19_1;
+    deduped_12_1 := HomalgIdentityMatrix( deduped_17_1, deduped_18_1 );
+    deduped_11_1 := deduped_19_1 * deduped_14_1;
+    deduped_10_1 := deduped_14_1 * deduped_17_1;
+    deduped_9_1 := deduped_13_1 * deduped_14_1;
+    deduped_8_1 := deduped_17_1 * deduped_9_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_9_1, deduped_18_1 );
+    hoisted_6_1 := deduped_20_1;
+    hoisted_5_1 := deduped_19_1;
+    hoisted_4_1 := deduped_14_1;
     hoisted_3_1 := deduped_9_1;
-    hoisted_2_1 := deduped_19_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_14_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+    hoisted_2_1 := deduped_17_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_12_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_20_1 ), deduped_7_1 ) * KroneckerMat( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_20_1 ) ) * KroneckerMat( TransposedMatrix( deduped_14_1 ), (KroneckerMat( deduped_10_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                          end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_20_1 ) ) * KroneckerMat( (KroneckerMat( deduped_10_1, deduped_14_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
+                      end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_18_1 ), deduped_7_1 ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_17_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_18_1 ) ) ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_17_1, (DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_13_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                              end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_18_1 ) ) ) * KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                                end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_20_1 ), deduped_14_1 ) * KroneckerMat( deduped_18_1, ConvertMatrixToColumn( deduped_14_1 ) )), deduped_12_1 ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_20_1 ) * (KroneckerMat( deduped_12_1, deduped_18_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_18_1 ), deduped_12_1 ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_19_1, ConvertMatrixToColumn( deduped_12_1 ) ) )), HomalgIdentityMatrix( deduped_14_1, deduped_18_1 ) ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                        end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_18_1 ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                               local deduped_1_2;
                               deduped_1_2 := (i_2 - 1);
                               return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                          end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_20_1 ), deduped_18_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_22_1, deduped_20_1 ), ConvertMatrixToColumn( deduped_18_1 ) ))) );
+                          end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_18_1 ), deduped_16_1 ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_20_1, ConvertMatrixToColumn( deduped_16_1 ) ) ))) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -3854,53 +3827,51 @@ end
         
 ########
 function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1;
-    deduped_22_1 := Dimension( c_1 );
-    deduped_21_1 := Dimension( b_1 );
-    deduped_20_1 := UnderlyingRing( cat_1 );
-    deduped_19_1 := Dimension( a_1 );
-    deduped_18_1 := HomalgIdentityMatrix( deduped_21_1, deduped_20_1 );
-    deduped_17_1 := deduped_19_1 * deduped_19_1;
-    deduped_16_1 := deduped_21_1 * deduped_22_1;
-    deduped_15_1 := deduped_19_1 * deduped_21_1;
-    deduped_14_1 := HomalgIdentityMatrix( deduped_19_1, deduped_20_1 );
-    deduped_13_1 := deduped_21_1 * deduped_16_1;
-    deduped_12_1 := HomalgIdentityMatrix( deduped_16_1, deduped_20_1 );
-    deduped_11_1 := deduped_16_1 * deduped_19_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_15_1, deduped_20_1 );
-    deduped_9_1 := deduped_15_1 * deduped_16_1;
-    deduped_8_1 := deduped_19_1 * deduped_9_1;
-    deduped_7_1 := HomalgIdentityMatrix( deduped_9_1, deduped_20_1 );
-    hoisted_6_1 := deduped_22_1;
-    hoisted_5_1 := deduped_21_1;
-    hoisted_4_1 := deduped_16_1;
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1;
+    deduped_20_1 := Dimension( c_1 );
+    deduped_19_1 := Dimension( b_1 );
+    deduped_18_1 := UnderlyingRing( cat_1 );
+    deduped_17_1 := Dimension( a_1 );
+    deduped_16_1 := HomalgIdentityMatrix( deduped_19_1, deduped_18_1 );
+    deduped_15_1 := deduped_17_1 * deduped_17_1;
+    deduped_14_1 := deduped_19_1 * deduped_20_1;
+    deduped_13_1 := deduped_17_1 * deduped_19_1;
+    deduped_12_1 := HomalgIdentityMatrix( deduped_17_1, deduped_18_1 );
+    deduped_11_1 := deduped_19_1 * deduped_14_1;
+    deduped_10_1 := deduped_14_1 * deduped_17_1;
+    deduped_9_1 := deduped_13_1 * deduped_14_1;
+    deduped_8_1 := deduped_17_1 * deduped_9_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_9_1, deduped_18_1 );
+    hoisted_6_1 := deduped_20_1;
+    hoisted_5_1 := deduped_19_1;
+    hoisted_4_1 := deduped_14_1;
     hoisted_3_1 := deduped_9_1;
-    hoisted_2_1 := deduped_19_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_14_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+    hoisted_2_1 := deduped_17_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_12_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_20_1 ), deduped_7_1 ) * KroneckerMat( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_20_1 ) ) * KroneckerMat( TransposedMatrix( deduped_14_1 ), (KroneckerMat( deduped_10_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                          end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_20_1 ) ) * KroneckerMat( (KroneckerMat( deduped_10_1, deduped_14_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
+                      end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_18_1 ), deduped_7_1 ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_17_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_18_1 ) ) ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_17_1, (DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_13_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                              end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_18_1 ) ) ) * KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                                end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_20_1 ), deduped_14_1 ) * KroneckerMat( deduped_18_1, ConvertMatrixToColumn( deduped_14_1 ) )), deduped_12_1 ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_20_1 ) * (KroneckerMat( deduped_12_1, deduped_18_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_18_1 ), deduped_12_1 ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_19_1, ConvertMatrixToColumn( deduped_12_1 ) ) )), HomalgIdentityMatrix( deduped_14_1, deduped_18_1 ) ) * HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                        end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_18_1 ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                               local deduped_1_2;
                               deduped_1_2 := (i_2 - 1);
                               return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                          end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_20_1 ), deduped_18_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_22_1, deduped_20_1 ), ConvertMatrixToColumn( deduped_18_1 ) ))) );
+                          end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_18_1 ), deduped_16_1 ) * DiagMat( deduped_18_1, ListWithIdenticalEntries( deduped_20_1, ConvertMatrixToColumn( deduped_16_1 ) ) ))) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -4757,11 +4728,11 @@ function ( cat_1, a_1 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_4_1 ) * KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_8_1 ) ) * KroneckerMat( TransposedMatrix( deduped_3_1 ), deduped_3_1 ) * ConvertMatrixToColumn( deduped_3_1 );
+                        end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_4_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_8_1 ) ) ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, deduped_3_1 ) ) * ConvertMatrixToColumn( deduped_3_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5182,50 +5153,46 @@ end
         
 ########
 function ( cat_1, a_1, b_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1;
-    deduped_23_1 := Dimension( b_1 );
-    deduped_22_1 := UnderlyingRing( cat_1 );
-    deduped_21_1 := Dimension( a_1 );
-    deduped_20_1 := HomalgIdentityMatrix( 1, deduped_22_1 );
-    deduped_19_1 := deduped_23_1 * 1;
-    deduped_18_1 := deduped_21_1 * 1;
-    deduped_17_1 := deduped_21_1 * deduped_23_1;
-    deduped_16_1 := HomalgIdentityMatrix( deduped_23_1, deduped_22_1 );
-    deduped_15_1 := HomalgIdentityMatrix( deduped_21_1, deduped_22_1 );
-    deduped_14_1 := HomalgIdentityMatrix( deduped_19_1, deduped_22_1 );
-    deduped_13_1 := deduped_19_1 * deduped_21_1;
-    deduped_12_1 := HomalgIdentityMatrix( deduped_18_1, deduped_22_1 );
-    deduped_11_1 := deduped_17_1 * deduped_17_1;
-    deduped_10_1 := deduped_18_1 * deduped_19_1;
-    deduped_9_1 := HomalgIdentityMatrix( deduped_17_1, deduped_22_1 );
-    deduped_8_1 := deduped_17_1 * deduped_10_1;
-    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_22_1 );
-    hoisted_6_1 := deduped_23_1;
-    hoisted_5_1 := deduped_19_1;
-    hoisted_4_1 := deduped_21_1;
-    hoisted_3_1 := deduped_10_1;
-    hoisted_2_1 := deduped_17_1;
-    morphism_attr_1_1 := KroneckerMat( deduped_15_1, deduped_16_1 ) * (KroneckerMat( ConvertMatrixToRow( deduped_9_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_22_1 ), deduped_7_1 ) * KroneckerMat( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1;
+    deduped_19_1 := UnderlyingRing( cat_1 );
+    deduped_18_1 := Dimension( b_1 );
+    deduped_17_1 := Dimension( a_1 );
+    deduped_16_1 := HomalgIdentityMatrix( deduped_17_1, deduped_19_1 );
+    deduped_15_1 := HomalgIdentityMatrix( deduped_18_1, deduped_19_1 );
+    deduped_14_1 := deduped_18_1 * 1;
+    deduped_13_1 := deduped_17_1 * 1;
+    deduped_12_1 := deduped_17_1 * deduped_18_1;
+    deduped_11_1 := deduped_14_1 * deduped_17_1;
+    deduped_10_1 := deduped_12_1 * deduped_12_1;
+    deduped_9_1 := deduped_13_1 * deduped_14_1;
+    deduped_8_1 := deduped_12_1 * deduped_9_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_9_1, deduped_19_1 );
+    hoisted_6_1 := deduped_18_1;
+    hoisted_5_1 := deduped_14_1;
+    hoisted_4_1 := deduped_17_1;
+    hoisted_3_1 := deduped_9_1;
+    hoisted_2_1 := deduped_12_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_12_1, deduped_19_1 ) ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_19_1 ), deduped_7_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_22_1 ) ) * KroneckerMat( TransposedMatrix( deduped_9_1 ), (KroneckerMat( KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                            end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_22_1 ) ), deduped_16_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_12_1, deduped_15_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                      local deduped_1_2;
-                                      deduped_1_2 := (i_2 - 1);
-                                      return (REM_INT( deduped_1_2, 1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                                  end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_22_1 ), deduped_15_1 ) * KroneckerMat( deduped_20_1, ConvertMatrixToColumn( deduped_15_1 ) )), deduped_14_1 ), deduped_16_1 ) * KroneckerMat( deduped_20_1, (KroneckerMat( deduped_14_1, deduped_16_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_19_1 ], function ( i_2 )
+                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_19_1 ) ) ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( deduped_12_1, (KroneckerMat( DiagMat( deduped_19_1, ListWithIdenticalEntries( deduped_13_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_19_1 ) ) ), deduped_15_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+                                    local deduped_1_2;
+                                    deduped_1_2 := (i_2 - 1);
+                                    return (REM_INT( deduped_1_2, 1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                                end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_19_1 ), deduped_16_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( 1, ConvertMatrixToColumn( deduped_16_1 ) ) )), HomalgIdentityMatrix( deduped_14_1, deduped_19_1 ) ), deduped_15_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( 1, (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, 1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                              end ) ), deduped_19_1 ), deduped_19_1, deduped_19_1, deduped_22_1 ), deduped_16_1 ) * KroneckerMat( deduped_20_1, ConvertMatrixToColumn( deduped_16_1 ) )) )) ));
+                              end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_19_1 ), deduped_15_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( 1, ConvertMatrixToColumn( deduped_15_1 ) ) )) ) )) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5237,50 +5204,46 @@ end
         
 ########
 function ( cat_1, s_1, a_1, b_1, r_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1;
-    deduped_23_1 := Dimension( b_1 );
-    deduped_22_1 := UnderlyingRing( cat_1 );
-    deduped_21_1 := Dimension( a_1 );
-    deduped_20_1 := HomalgIdentityMatrix( 1, deduped_22_1 );
-    deduped_19_1 := deduped_23_1 * 1;
-    deduped_18_1 := deduped_21_1 * 1;
-    deduped_17_1 := deduped_21_1 * deduped_23_1;
-    deduped_16_1 := HomalgIdentityMatrix( deduped_23_1, deduped_22_1 );
-    deduped_15_1 := HomalgIdentityMatrix( deduped_21_1, deduped_22_1 );
-    deduped_14_1 := HomalgIdentityMatrix( deduped_19_1, deduped_22_1 );
-    deduped_13_1 := deduped_19_1 * deduped_21_1;
-    deduped_12_1 := HomalgIdentityMatrix( deduped_18_1, deduped_22_1 );
-    deduped_11_1 := deduped_17_1 * deduped_17_1;
-    deduped_10_1 := deduped_18_1 * deduped_19_1;
-    deduped_9_1 := HomalgIdentityMatrix( deduped_17_1, deduped_22_1 );
-    deduped_8_1 := deduped_17_1 * deduped_10_1;
-    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_22_1 );
-    hoisted_6_1 := deduped_23_1;
-    hoisted_5_1 := deduped_19_1;
-    hoisted_4_1 := deduped_21_1;
-    hoisted_3_1 := deduped_10_1;
-    hoisted_2_1 := deduped_17_1;
-    morphism_attr_1_1 := KroneckerMat( deduped_15_1, deduped_16_1 ) * (KroneckerMat( ConvertMatrixToRow( deduped_9_1 ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_22_1 ), deduped_7_1 ) * KroneckerMat( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1;
+    deduped_19_1 := UnderlyingRing( cat_1 );
+    deduped_18_1 := Dimension( b_1 );
+    deduped_17_1 := Dimension( a_1 );
+    deduped_16_1 := HomalgIdentityMatrix( deduped_17_1, deduped_19_1 );
+    deduped_15_1 := HomalgIdentityMatrix( deduped_18_1, deduped_19_1 );
+    deduped_14_1 := deduped_18_1 * 1;
+    deduped_13_1 := deduped_17_1 * 1;
+    deduped_12_1 := deduped_17_1 * deduped_18_1;
+    deduped_11_1 := deduped_14_1 * deduped_17_1;
+    deduped_10_1 := deduped_12_1 * deduped_12_1;
+    deduped_9_1 := deduped_13_1 * deduped_14_1;
+    deduped_8_1 := deduped_12_1 * deduped_9_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_9_1, deduped_19_1 );
+    hoisted_6_1 := deduped_18_1;
+    hoisted_5_1 := deduped_14_1;
+    hoisted_4_1 := deduped_17_1;
+    hoisted_3_1 := deduped_9_1;
+    hoisted_2_1 := deduped_12_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_12_1, deduped_19_1 ) ), deduped_7_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_19_1 ), deduped_7_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_22_1 ) ) * KroneckerMat( TransposedMatrix( deduped_9_1 ), (KroneckerMat( KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                            end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_22_1 ) ), deduped_16_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_12_1, deduped_15_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
-                                      local deduped_1_2;
-                                      deduped_1_2 := (i_2 - 1);
-                                      return (REM_INT( deduped_1_2, 1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                                  end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_22_1 ), deduped_15_1 ) * KroneckerMat( deduped_20_1, ConvertMatrixToColumn( deduped_15_1 ) )), deduped_14_1 ), deduped_16_1 ) * KroneckerMat( deduped_20_1, (KroneckerMat( deduped_14_1, deduped_16_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_19_1 ], function ( i_2 )
+                      end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_19_1 ) ) ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( deduped_12_1, (KroneckerMat( DiagMat( deduped_19_1, ListWithIdenticalEntries( deduped_13_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_19_1 ) ) ), deduped_15_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+                                    local deduped_1_2;
+                                    deduped_1_2 := (i_2 - 1);
+                                    return (REM_INT( deduped_1_2, 1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                                end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_19_1 ), deduped_16_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( 1, ConvertMatrixToColumn( deduped_16_1 ) ) )), HomalgIdentityMatrix( deduped_14_1, deduped_19_1 ) ), deduped_15_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( 1, (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, 1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                              end ) ), deduped_19_1 ), deduped_19_1, deduped_19_1, deduped_22_1 ), deduped_16_1 ) * KroneckerMat( deduped_20_1, ConvertMatrixToColumn( deduped_16_1 ) )) )) ));
+                              end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_19_1 ), deduped_15_1 ) * DiagMat( deduped_19_1, ListWithIdenticalEntries( 1, ConvertMatrixToColumn( deduped_15_1 ) ) )) ) )) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5292,55 +5255,51 @@ end
         
 ########
 function ( cat_1, list_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1, deduped_27_1, deduped_28_1;
-    deduped_28_1 := UnderlyingRing( cat_1 );
-    deduped_27_1 := List( list_1, Dimension );
-    deduped_26_1 := deduped_27_1[4];
-    deduped_25_1 := deduped_27_1[2];
-    deduped_24_1 := deduped_27_1[3];
-    deduped_23_1 := deduped_27_1[1];
-    deduped_22_1 := HomalgIdentityMatrix( deduped_25_1, deduped_28_1 );
-    deduped_21_1 := HomalgIdentityMatrix( deduped_23_1, deduped_28_1 );
-    deduped_20_1 := HomalgIdentityMatrix( deduped_24_1, deduped_28_1 );
-    deduped_19_1 := deduped_24_1 * deduped_26_1;
-    deduped_18_1 := deduped_23_1 * deduped_25_1;
-    deduped_17_1 := deduped_23_1 * deduped_24_1;
-    deduped_16_1 := HomalgIdentityMatrix( deduped_19_1, deduped_28_1 );
-    deduped_15_1 := deduped_19_1 * deduped_23_1;
-    deduped_14_1 := HomalgIdentityMatrix( deduped_18_1, deduped_28_1 );
-    deduped_13_1 := deduped_17_1 * deduped_17_1;
-    deduped_12_1 := deduped_18_1 * deduped_19_1;
-    deduped_11_1 := HomalgIdentityMatrix( deduped_17_1, deduped_28_1 );
-    deduped_10_1 := deduped_17_1 * deduped_12_1;
-    deduped_9_1 := HomalgIdentityMatrix( deduped_12_1, deduped_28_1 );
-    hoisted_8_1 := deduped_24_1;
-    hoisted_7_1 := deduped_26_1;
-    hoisted_6_1 := deduped_25_1;
-    hoisted_5_1 := deduped_19_1;
-    hoisted_4_1 := deduped_23_1;
-    hoisted_3_1 := deduped_12_1;
-    hoisted_2_1 := deduped_17_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_11_1 ), deduped_9_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1;
+    deduped_24_1 := UnderlyingRing( cat_1 );
+    deduped_23_1 := List( list_1, Dimension );
+    deduped_22_1 := deduped_23_1[4];
+    deduped_21_1 := deduped_23_1[2];
+    deduped_20_1 := deduped_23_1[3];
+    deduped_19_1 := deduped_23_1[1];
+    deduped_18_1 := HomalgIdentityMatrix( deduped_19_1, deduped_24_1 );
+    deduped_17_1 := HomalgIdentityMatrix( deduped_20_1, deduped_24_1 );
+    deduped_16_1 := deduped_20_1 * deduped_22_1;
+    deduped_15_1 := deduped_19_1 * deduped_21_1;
+    deduped_14_1 := deduped_19_1 * deduped_20_1;
+    deduped_13_1 := deduped_16_1 * deduped_19_1;
+    deduped_12_1 := deduped_14_1 * deduped_14_1;
+    deduped_11_1 := deduped_15_1 * deduped_16_1;
+    deduped_10_1 := deduped_14_1 * deduped_11_1;
+    deduped_9_1 := HomalgIdentityMatrix( deduped_11_1, deduped_24_1 );
+    hoisted_8_1 := deduped_20_1;
+    hoisted_7_1 := deduped_22_1;
+    hoisted_6_1 := deduped_21_1;
+    hoisted_5_1 := deduped_16_1;
+    hoisted_4_1 := deduped_19_1;
+    hoisted_3_1 := deduped_11_1;
+    hoisted_2_1 := deduped_14_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_14_1, deduped_24_1 ) ), deduped_9_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_28_1 ), deduped_9_1 ) * KroneckerMat( deduped_11_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_28_1 ) ) * KroneckerMat( TransposedMatrix( deduped_11_1 ), (KroneckerMat( KroneckerMat( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                          end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_28_1 ) ), deduped_20_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_14_1, deduped_21_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
+                      end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_24_1 ), deduped_9_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_24_1 ) ) ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_14_1, (KroneckerMat( DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_24_1 ) ) ), deduped_17_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                                end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_28_1 ), deduped_21_1 ) * KroneckerMat( deduped_22_1, ConvertMatrixToColumn( deduped_21_1 ) )), deduped_16_1 ), deduped_20_1 ) * KroneckerMat( deduped_22_1, (KroneckerMat( deduped_16_1, deduped_20_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_19_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                            end ) ), deduped_19_1 ), deduped_19_1, deduped_19_1, deduped_28_1 ), deduped_20_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_26_1, deduped_28_1 ), ConvertMatrixToColumn( deduped_20_1 ) )) )) );
+                                end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_24_1 ), deduped_18_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_21_1, ConvertMatrixToColumn( deduped_18_1 ) ) )), HomalgIdentityMatrix( deduped_16_1, deduped_24_1 ) ), deduped_17_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_21_1, (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
+                              end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_24_1 ), deduped_17_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToColumn( deduped_17_1 ) ) )) ) )) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5352,56 +5311,52 @@ end
         
 ########
 function ( cat_1, list_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1, deduped_27_1, deduped_28_1, deduped_29_1;
-    deduped_29_1 := UnderlyingRing( cat_1 );
-    deduped_28_1 := List( list_1, Dimension );
-    deduped_27_1 := deduped_28_1[4];
-    deduped_26_1 := deduped_28_1[2];
-    deduped_25_1 := deduped_28_1[3];
-    deduped_24_1 := deduped_28_1[1];
-    deduped_23_1 := HomalgIdentityMatrix( deduped_26_1, deduped_29_1 );
-    deduped_22_1 := HomalgIdentityMatrix( deduped_24_1, deduped_29_1 );
-    deduped_21_1 := HomalgIdentityMatrix( deduped_25_1, deduped_29_1 );
-    deduped_20_1 := deduped_25_1 * deduped_27_1;
-    deduped_19_1 := deduped_24_1 * deduped_26_1;
-    deduped_18_1 := deduped_24_1 * deduped_25_1;
-    deduped_17_1 := deduped_18_1 * deduped_18_1;
-    deduped_16_1 := deduped_19_1 * deduped_20_1;
-    deduped_15_1 := HomalgIdentityMatrix( deduped_20_1, deduped_29_1 );
-    deduped_14_1 := deduped_20_1 * deduped_24_1;
-    deduped_13_1 := HomalgIdentityMatrix( deduped_19_1, deduped_29_1 );
-    deduped_12_1 := HomalgIdentityMatrix( deduped_18_1, deduped_29_1 );
-    deduped_11_1 := deduped_18_1 * deduped_16_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_16_1, deduped_29_1 );
-    hoisted_6_1 := deduped_25_1;
-    hoisted_5_1 := deduped_27_1;
-    hoisted_4_1 := deduped_26_1;
-    hoisted_3_1 := deduped_20_1;
-    hoisted_2_1 := deduped_24_1;
-    deduped_9_1 := KroneckerMat( TransposedMatrix( deduped_12_1 ), KroneckerMat( KroneckerMat( deduped_13_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_29_1 ) ), deduped_21_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_13_1, deduped_22_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_19_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1;
+    deduped_25_1 := List( list_1, Dimension );
+    deduped_24_1 := UnderlyingRing( cat_1 );
+    deduped_23_1 := deduped_25_1[4];
+    deduped_22_1 := deduped_25_1[2];
+    deduped_21_1 := deduped_25_1[3];
+    deduped_20_1 := deduped_25_1[1];
+    deduped_19_1 := HomalgIdentityMatrix( deduped_20_1, deduped_24_1 );
+    deduped_18_1 := HomalgIdentityMatrix( deduped_21_1, deduped_24_1 );
+    deduped_17_1 := deduped_21_1 * deduped_23_1;
+    deduped_16_1 := deduped_20_1 * deduped_22_1;
+    deduped_15_1 := deduped_20_1 * deduped_21_1;
+    deduped_14_1 := deduped_15_1 * deduped_15_1;
+    deduped_13_1 := deduped_16_1 * deduped_17_1;
+    deduped_12_1 := deduped_17_1 * deduped_20_1;
+    deduped_11_1 := deduped_15_1 * deduped_13_1;
+    deduped_10_1 := HomalgIdentityMatrix( deduped_13_1, deduped_24_1 );
+    hoisted_6_1 := deduped_21_1;
+    hoisted_5_1 := deduped_23_1;
+    hoisted_4_1 := deduped_22_1;
+    hoisted_3_1 := deduped_17_1;
+    hoisted_2_1 := deduped_20_1;
+    deduped_9_1 := DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, KroneckerMat( DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_16_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                            end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_24_1 ) ) ), deduped_18_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                              end ) ), deduped_19_1 ), deduped_19_1, deduped_19_1, deduped_29_1 ), deduped_22_1 ) * KroneckerMat( deduped_23_1, ConvertMatrixToColumn( deduped_22_1 ) )), deduped_15_1 ), deduped_21_1 ) * KroneckerMat( deduped_23_1, (KroneckerMat( deduped_15_1, deduped_21_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_20_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                          end ) ), deduped_20_1 ), deduped_20_1, deduped_20_1, deduped_29_1 ), deduped_21_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_27_1, deduped_29_1 ), ConvertMatrixToColumn( deduped_21_1 ) )) ) );
-    hoisted_8_1 := deduped_16_1;
-    hoisted_7_1 := deduped_18_1;
-    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_29_1 ), KroneckerMat( ConvertMatrixToRow( deduped_12_1 ), deduped_10_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                              end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_24_1 ), deduped_19_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToColumn( deduped_19_1 ) ) )), HomalgIdentityMatrix( deduped_17_1, deduped_24_1 ) ), deduped_18_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
+                            end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_24_1 ), deduped_18_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_23_1, ConvertMatrixToColumn( deduped_18_1 ) ) )) ) ) ) );
+    hoisted_8_1 := deduped_13_1;
+    hoisted_7_1 := deduped_15_1;
+    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_24_1 ), KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_15_1, deduped_24_1 ) ), deduped_10_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                        end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_29_1 ), deduped_10_1 ) * KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
-                      end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_29_1 ) ) * deduped_9_1 );
+                        end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_24_1 ), deduped_10_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
+                        end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_24_1 ) ) ) * deduped_9_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5413,56 +5368,52 @@ end
         
 ########
 function ( cat_1, source_1, list_1, range_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1, deduped_27_1, deduped_28_1, deduped_29_1;
-    deduped_29_1 := UnderlyingRing( cat_1 );
-    deduped_28_1 := List( list_1, Dimension );
-    deduped_27_1 := deduped_28_1[4];
-    deduped_26_1 := deduped_28_1[2];
-    deduped_25_1 := deduped_28_1[3];
-    deduped_24_1 := deduped_28_1[1];
-    deduped_23_1 := HomalgIdentityMatrix( deduped_26_1, deduped_29_1 );
-    deduped_22_1 := HomalgIdentityMatrix( deduped_24_1, deduped_29_1 );
-    deduped_21_1 := HomalgIdentityMatrix( deduped_25_1, deduped_29_1 );
-    deduped_20_1 := deduped_25_1 * deduped_27_1;
-    deduped_19_1 := deduped_24_1 * deduped_26_1;
-    deduped_18_1 := deduped_24_1 * deduped_25_1;
-    deduped_17_1 := deduped_18_1 * deduped_18_1;
-    deduped_16_1 := deduped_19_1 * deduped_20_1;
-    deduped_15_1 := HomalgIdentityMatrix( deduped_20_1, deduped_29_1 );
-    deduped_14_1 := deduped_20_1 * deduped_24_1;
-    deduped_13_1 := HomalgIdentityMatrix( deduped_19_1, deduped_29_1 );
-    deduped_12_1 := HomalgIdentityMatrix( deduped_18_1, deduped_29_1 );
-    deduped_11_1 := deduped_18_1 * deduped_16_1;
-    deduped_10_1 := HomalgIdentityMatrix( deduped_16_1, deduped_29_1 );
-    hoisted_6_1 := deduped_25_1;
-    hoisted_5_1 := deduped_27_1;
-    hoisted_4_1 := deduped_26_1;
-    hoisted_3_1 := deduped_20_1;
-    hoisted_2_1 := deduped_24_1;
-    deduped_9_1 := KroneckerMat( TransposedMatrix( deduped_12_1 ), KroneckerMat( KroneckerMat( deduped_13_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
-                            local deduped_1_2;
-                            deduped_1_2 := (i_2 - 1);
-                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_29_1 ) ), deduped_21_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_13_1, deduped_22_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_19_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1;
+    deduped_25_1 := List( list_1, Dimension );
+    deduped_24_1 := UnderlyingRing( cat_1 );
+    deduped_23_1 := deduped_25_1[4];
+    deduped_22_1 := deduped_25_1[2];
+    deduped_21_1 := deduped_25_1[3];
+    deduped_20_1 := deduped_25_1[1];
+    deduped_19_1 := HomalgIdentityMatrix( deduped_20_1, deduped_24_1 );
+    deduped_18_1 := HomalgIdentityMatrix( deduped_21_1, deduped_24_1 );
+    deduped_17_1 := deduped_21_1 * deduped_23_1;
+    deduped_16_1 := deduped_20_1 * deduped_22_1;
+    deduped_15_1 := deduped_20_1 * deduped_21_1;
+    deduped_14_1 := deduped_15_1 * deduped_15_1;
+    deduped_13_1 := deduped_16_1 * deduped_17_1;
+    deduped_12_1 := deduped_17_1 * deduped_20_1;
+    deduped_11_1 := deduped_15_1 * deduped_13_1;
+    deduped_10_1 := HomalgIdentityMatrix( deduped_13_1, deduped_24_1 );
+    hoisted_6_1 := deduped_21_1;
+    hoisted_5_1 := deduped_23_1;
+    hoisted_4_1 := deduped_22_1;
+    hoisted_3_1 := deduped_17_1;
+    hoisted_2_1 := deduped_20_1;
+    deduped_9_1 := DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, KroneckerMat( DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_16_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                            end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_24_1 ) ) ), deduped_18_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
                                   local deduped_1_2;
                                   deduped_1_2 := (i_2 - 1);
                                   return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                              end ) ), deduped_19_1 ), deduped_19_1, deduped_19_1, deduped_29_1 ), deduped_22_1 ) * KroneckerMat( deduped_23_1, ConvertMatrixToColumn( deduped_22_1 ) )), deduped_15_1 ), deduped_21_1 ) * KroneckerMat( deduped_23_1, (KroneckerMat( deduped_15_1, deduped_21_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_20_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
-                          end ) ), deduped_20_1 ), deduped_20_1, deduped_20_1, deduped_29_1 ), deduped_21_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_27_1, deduped_29_1 ), ConvertMatrixToColumn( deduped_21_1 ) )) ) );
-    hoisted_8_1 := deduped_16_1;
-    hoisted_7_1 := deduped_18_1;
-    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_29_1 ), KroneckerMat( ConvertMatrixToRow( deduped_12_1 ), deduped_10_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                              end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_24_1 ), deduped_19_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToColumn( deduped_19_1 ) ) )), HomalgIdentityMatrix( deduped_17_1, deduped_24_1 ) ), deduped_18_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_17_1 ], function ( i_2 )
+                                local deduped_1_2;
+                                deduped_1_2 := (i_2 - 1);
+                                return (REM_INT( deduped_1_2, hoisted_5_1 ) * hoisted_6_1 + QUO_INT( deduped_1_2, hoisted_5_1 ) + 1);
+                            end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_24_1 ), deduped_18_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_23_1, ConvertMatrixToColumn( deduped_18_1 ) ) )) ) ) ) );
+    hoisted_8_1 := deduped_13_1;
+    hoisted_7_1 := deduped_15_1;
+    morphism_attr_1_1 := RightDivide( HomalgIdentityMatrix( NumberColumns( deduped_9_1 ), deduped_24_1 ), KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_15_1, deduped_24_1 ) ), deduped_10_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_14_1 ], function ( i_2 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                        end ) ), deduped_17_1 ), deduped_17_1, deduped_17_1, deduped_29_1 ), deduped_10_1 ) * KroneckerMat( deduped_12_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
-                      end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_29_1 ) ) * deduped_9_1 );
+                        end ) ), deduped_14_1 ), deduped_14_1, deduped_14_1, deduped_24_1 ), deduped_10_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_11_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_8_1 ) * hoisted_7_1 + QUO_INT( deduped_1_2, hoisted_8_1 ) + 1);
+                        end ) ), deduped_11_1 ), deduped_11_1, deduped_11_1, deduped_24_1 ) ) ) * deduped_9_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5474,55 +5425,51 @@ end
         
 ########
 function ( cat_1, source_1, list_1, range_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1, deduped_25_1, deduped_26_1, deduped_27_1, deduped_28_1;
-    deduped_28_1 := UnderlyingRing( cat_1 );
-    deduped_27_1 := List( list_1, Dimension );
-    deduped_26_1 := deduped_27_1[4];
-    deduped_25_1 := deduped_27_1[2];
-    deduped_24_1 := deduped_27_1[3];
-    deduped_23_1 := deduped_27_1[1];
-    deduped_22_1 := HomalgIdentityMatrix( deduped_25_1, deduped_28_1 );
-    deduped_21_1 := HomalgIdentityMatrix( deduped_23_1, deduped_28_1 );
-    deduped_20_1 := HomalgIdentityMatrix( deduped_24_1, deduped_28_1 );
-    deduped_19_1 := deduped_24_1 * deduped_26_1;
-    deduped_18_1 := deduped_23_1 * deduped_25_1;
-    deduped_17_1 := deduped_23_1 * deduped_24_1;
-    deduped_16_1 := HomalgIdentityMatrix( deduped_19_1, deduped_28_1 );
-    deduped_15_1 := deduped_19_1 * deduped_23_1;
-    deduped_14_1 := HomalgIdentityMatrix( deduped_18_1, deduped_28_1 );
-    deduped_13_1 := deduped_17_1 * deduped_17_1;
-    deduped_12_1 := deduped_18_1 * deduped_19_1;
-    deduped_11_1 := HomalgIdentityMatrix( deduped_17_1, deduped_28_1 );
-    deduped_10_1 := deduped_17_1 * deduped_12_1;
-    deduped_9_1 := HomalgIdentityMatrix( deduped_12_1, deduped_28_1 );
-    hoisted_8_1 := deduped_24_1;
-    hoisted_7_1 := deduped_26_1;
-    hoisted_6_1 := deduped_25_1;
-    hoisted_5_1 := deduped_19_1;
-    hoisted_4_1 := deduped_23_1;
-    hoisted_3_1 := deduped_12_1;
-    hoisted_2_1 := deduped_17_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_11_1 ), deduped_9_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, hoisted_6_1, hoisted_7_1, hoisted_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1, deduped_15_1, deduped_16_1, deduped_17_1, deduped_18_1, deduped_19_1, deduped_20_1, deduped_21_1, deduped_22_1, deduped_23_1, deduped_24_1;
+    deduped_24_1 := UnderlyingRing( cat_1 );
+    deduped_23_1 := List( list_1, Dimension );
+    deduped_22_1 := deduped_23_1[4];
+    deduped_21_1 := deduped_23_1[2];
+    deduped_20_1 := deduped_23_1[3];
+    deduped_19_1 := deduped_23_1[1];
+    deduped_18_1 := HomalgIdentityMatrix( deduped_19_1, deduped_24_1 );
+    deduped_17_1 := HomalgIdentityMatrix( deduped_20_1, deduped_24_1 );
+    deduped_16_1 := deduped_20_1 * deduped_22_1;
+    deduped_15_1 := deduped_19_1 * deduped_21_1;
+    deduped_14_1 := deduped_19_1 * deduped_20_1;
+    deduped_13_1 := deduped_16_1 * deduped_19_1;
+    deduped_12_1 := deduped_14_1 * deduped_14_1;
+    deduped_11_1 := deduped_15_1 * deduped_16_1;
+    deduped_10_1 := deduped_14_1 * deduped_11_1;
+    deduped_9_1 := HomalgIdentityMatrix( deduped_11_1, deduped_24_1 );
+    hoisted_8_1 := deduped_20_1;
+    hoisted_7_1 := deduped_22_1;
+    hoisted_6_1 := deduped_21_1;
+    hoisted_5_1 := deduped_16_1;
+    hoisted_4_1 := deduped_19_1;
+    hoisted_3_1 := deduped_11_1;
+    hoisted_2_1 := deduped_14_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_14_1, deduped_24_1 ) ), deduped_9_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_12_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_28_1 ), deduped_9_1 ) * KroneckerMat( deduped_11_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_28_1 ) ) * KroneckerMat( TransposedMatrix( deduped_11_1 ), (KroneckerMat( KroneckerMat( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
-                              local deduped_1_2;
-                              deduped_1_2 := (i_2 - 1);
-                              return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
-                          end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_28_1 ) ), deduped_20_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( deduped_14_1, deduped_21_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_18_1 ], function ( i_2 )
+                      end ) ), deduped_12_1 ), deduped_12_1, deduped_12_1, deduped_24_1 ), deduped_9_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_14_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_10_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_10_1 ), deduped_10_1, deduped_10_1, deduped_24_1 ) ) ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_14_1, (KroneckerMat( DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_15_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_13_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_4_1 ) * hoisted_5_1 + QUO_INT( deduped_1_2, hoisted_4_1 ) + 1);
+                              end ) ), deduped_13_1 ), deduped_13_1, deduped_13_1, deduped_24_1 ) ) ), deduped_17_1 ) * KroneckerMat( KroneckerMat( (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_15_1 ], function ( i_2 )
                                     local deduped_1_2;
                                     deduped_1_2 := (i_2 - 1);
                                     return (REM_INT( deduped_1_2, hoisted_6_1 ) * hoisted_4_1 + QUO_INT( deduped_1_2, hoisted_6_1 ) + 1);
-                                end ) ), deduped_18_1 ), deduped_18_1, deduped_18_1, deduped_28_1 ), deduped_21_1 ) * KroneckerMat( deduped_22_1, ConvertMatrixToColumn( deduped_21_1 ) )), deduped_16_1 ), deduped_20_1 ) * KroneckerMat( deduped_22_1, (KroneckerMat( deduped_16_1, deduped_20_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_19_1 ], function ( i_2 )
-                                local deduped_1_2;
-                                deduped_1_2 := (i_2 - 1);
-                                return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
-                            end ) ), deduped_19_1 ), deduped_19_1, deduped_19_1, deduped_28_1 ), deduped_20_1 ) * KroneckerMat( HomalgIdentityMatrix( deduped_26_1, deduped_28_1 ), ConvertMatrixToColumn( deduped_20_1 ) )) )) );
+                                end ) ), deduped_15_1 ), deduped_15_1, deduped_15_1, deduped_24_1 ), deduped_18_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_21_1, ConvertMatrixToColumn( deduped_18_1 ) ) )), HomalgIdentityMatrix( deduped_16_1, deduped_24_1 ) ), deduped_17_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_21_1, (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_16_1 ], function ( i_2 )
+                                  local deduped_1_2;
+                                  deduped_1_2 := (i_2 - 1);
+                                  return (REM_INT( deduped_1_2, hoisted_7_1 ) * hoisted_8_1 + QUO_INT( deduped_1_2, hoisted_7_1 ) + 1);
+                              end ) ), deduped_16_1 ), deduped_16_1, deduped_16_1, deduped_24_1 ), deduped_17_1 ) * DiagMat( deduped_24_1, ListWithIdenticalEntries( deduped_22_1, ConvertMatrixToColumn( deduped_17_1 ) ) )) ) )) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5569,25 +5516,24 @@ end
         
 ########
 function ( cat_1, c_1, b_1, g_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( c_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( c_1 );
     deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := deduped_10_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( deduped_9_1, deduped_7_1 );
+    deduped_5_1 := deduped_8_1 * deduped_8_1;
+    deduped_4_1 := deduped_9_1 * deduped_8_1;
+    hoisted_3_1 := deduped_9_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_4_1 ), UnderlyingMatrix( g_1 ) ) * (KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_9_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, UnderlyingMatrix( g_1 ) ) ) * (DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_4_1 ), deduped_7_1 ));
+                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_6_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_8_1, deduped_7_1 ) ), deduped_6_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5599,25 +5545,24 @@ end
         
 ########
 function ( cat_1, a_1, b_1, f_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( a_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
-    deduped_8_1 := Dimension( b_1 );
-    deduped_7_1 := deduped_8_1 * deduped_10_1;
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
-    hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_4_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( a_1 );
+    deduped_8_1 := UnderlyingRing( cat_1 );
+    deduped_7_1 := Dimension( b_1 );
+    deduped_6_1 := deduped_7_1 * deduped_9_1;
+    deduped_5_1 := deduped_7_1 * deduped_7_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_9_1, deduped_8_1 );
+    hoisted_3_1 := deduped_9_1;
+    hoisted_2_1 := deduped_7_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_7_1, deduped_8_1 ) ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_5_1 ) * KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_9_1 ) ) * KroneckerMat( TransposedMatrix( deduped_4_1 ), UnderlyingMatrix( f_1 ) );
+                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_4_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_8_1 ) ) ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, UnderlyingMatrix( f_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -5688,11 +5633,11 @@ function ( cat_1, alpha_1 )
                             local deduped_1_2;
                             deduped_1_2 := (i_2 - 1);
                             return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_7_1 ) * KroneckerMat( deduped_3_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ) ) * KroneckerMat( TransposedMatrix( deduped_3_1 ), UnderlyingMatrix( alpha_1 ) ) * ConvertMatrixToColumn( deduped_3_1 );
+                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_8_1 ), deduped_7_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_6_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, 1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, 1 ) + 1);
+                        end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ) ) ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_6_1, UnderlyingMatrix( alpha_1 ) ) ) * ConvertMatrixToColumn( deduped_3_1 );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -6066,25 +6011,24 @@ end
         
 ########
 function ( cat_1, t_1, a_1, alpha_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( t_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( t_1 );
     deduped_8_1 := Dimension( a_1 );
-    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := deduped_10_1 * deduped_8_1;
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
+    deduped_7_1 := UnderlyingRing( cat_1 );
+    deduped_6_1 := HomalgIdentityMatrix( deduped_9_1, deduped_7_1 );
+    deduped_5_1 := deduped_8_1 * deduped_8_1;
+    deduped_4_1 := deduped_9_1 * deduped_8_1;
+    hoisted_3_1 := deduped_9_1;
     hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( TransposedMatrix( deduped_4_1 ), UnderlyingMatrix( alpha_1 ) ) * (KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
-                          local deduped_1_2;
-                          deduped_1_2 := (i_2 - 1);
-                          return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_9_1 ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    morphism_attr_1_1 := DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, UnderlyingMatrix( alpha_1 ) ) ) * (DiagMat( deduped_7_1, ListWithIdenticalEntries( deduped_8_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_4_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_3_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                        end ) ), deduped_4_1 ), deduped_4_1, deduped_4_1, deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_7_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_4_1 ), deduped_7_1 ));
+                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_7_1 ), deduped_6_1 ) * KroneckerMat( ConvertMatrixToColumn( HomalgIdentityMatrix( deduped_8_1, deduped_7_1 ) ), deduped_6_1 ));
     return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberColumns( morphism_attr_1_1 ) ), UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
@@ -6096,25 +6040,24 @@ end
         
 ########
 function ( cat_1, t_1, a_1, alpha_1 )
-    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1;
-    deduped_10_1 := Dimension( t_1 );
-    deduped_9_1 := UnderlyingRing( cat_1 );
-    deduped_8_1 := Dimension( a_1 );
-    deduped_7_1 := deduped_8_1 * deduped_10_1;
-    deduped_6_1 := deduped_8_1 * deduped_8_1;
-    deduped_5_1 := HomalgIdentityMatrix( deduped_10_1, deduped_9_1 );
-    deduped_4_1 := HomalgIdentityMatrix( deduped_8_1, deduped_9_1 );
-    hoisted_3_1 := deduped_10_1;
-    hoisted_2_1 := deduped_8_1;
-    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( deduped_4_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+    local morphism_attr_1_1, hoisted_2_1, hoisted_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1;
+    deduped_9_1 := Dimension( t_1 );
+    deduped_8_1 := UnderlyingRing( cat_1 );
+    deduped_7_1 := Dimension( a_1 );
+    deduped_6_1 := deduped_7_1 * deduped_9_1;
+    deduped_5_1 := deduped_7_1 * deduped_7_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_9_1, deduped_8_1 );
+    hoisted_3_1 := deduped_9_1;
+    hoisted_2_1 := deduped_7_1;
+    morphism_attr_1_1 := KroneckerMat( ConvertMatrixToRow( HomalgIdentityMatrix( deduped_7_1, deduped_8_1 ) ), deduped_4_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_5_1 ], function ( i_2 )
                           local deduped_1_2;
                           deduped_1_2 := (i_2 - 1);
                           return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
-                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_9_1 ), deduped_5_1 ) * KroneckerMat( deduped_4_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
-                        local deduped_1_2;
-                        deduped_1_2 := (i_2 - 1);
-                        return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
-                    end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_9_1 ) ) * KroneckerMat( TransposedMatrix( deduped_4_1 ), UnderlyingMatrix( alpha_1 ) );
+                      end ) ), deduped_5_1 ), deduped_5_1, deduped_5_1, deduped_8_1 ), deduped_4_1 ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                          local deduped_1_2;
+                          deduped_1_2 := (i_2 - 1);
+                          return (REM_INT( deduped_1_2, hoisted_3_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_3_1 ) + 1);
+                      end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_8_1 ) ) ) * DiagMat( deduped_8_1, ListWithIdenticalEntries( deduped_7_1, UnderlyingMatrix( alpha_1 ) ) );
     return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Dimension, NumberRows( morphism_attr_1_1 ) ), a_1, UnderlyingMatrix, morphism_attr_1_1 );
 end
 ########
diff --git a/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfArbitraryRingPrecompiled.gi b/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfArbitraryRingPrecompiled.gi
index 624c67774d..83fc831c24 100644
--- a/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfArbitraryRingPrecompiled.gi
+++ b/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfArbitraryRingPrecompiled.gi
@@ -129,6 +129,25 @@ end
         
     , 100 );
     
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) and NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
         
@@ -140,6 +159,42 @@ end
         
     , 100 );
     
+    ##
+    AddKernelEmbedding( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := Source( alpha_1 );
+    deduped_1_1 := ReducedSyzygiesOfRows( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( Range( alpha_1 ) ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfRows( deduped_1_1, UnderlyingMatrix( deduped_2_1 ) ) ), deduped_2_1, UnderlyingMatrix, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLiftAlongMonomorphism( cat,
+        
+########
+function ( cat_1, iota_1, tau_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( tau_1 ), Source( iota_1 ), UnderlyingMatrix, RightDivide( UnderlyingMatrix( tau_1 ), UnderlyingMatrix( iota_1 ), UnderlyingMatrix( Range( iota_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( alpha_1 ) * UnderlyingMatrix( beta_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
         
diff --git a/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfCommutativeRingPrecompiled.gi b/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfCommutativeRingPrecompiled.gi
index 3e5692d3d2..e043bb4ae4 100644
--- a/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfCommutativeRingPrecompiled.gi
+++ b/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfCommutativeRingPrecompiled.gi
@@ -129,6 +129,25 @@ end
         
     , 100 );
     
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) and NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
         
@@ -140,6 +159,42 @@ end
         
     , 100 );
     
+    ##
+    AddKernelEmbedding( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := Source( alpha_1 );
+    deduped_1_1 := ReducedSyzygiesOfRows( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( Range( alpha_1 ) ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfRows( deduped_1_1, UnderlyingMatrix( deduped_2_1 ) ) ), deduped_2_1, UnderlyingMatrix, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLiftAlongMonomorphism( cat,
+        
+########
+function ( cat_1, iota_1, tau_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( tau_1 ), Source( iota_1 ), UnderlyingMatrix, RightDivide( UnderlyingMatrix( tau_1 ), UnderlyingMatrix( iota_1 ), UnderlyingMatrix( Range( iota_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( alpha_1 ) * UnderlyingMatrix( beta_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
         
@@ -223,6 +278,155 @@ end
         
     , 100 );
     
+    ##
+    AddAssociatorLeftToRightWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddAssociatorRightToLeftWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddBraidingWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := NumberColumns( UnderlyingMatrix( b_1 ) );
+    deduped_4_1 := NumberColumns( UnderlyingMatrix( a_1 ) );
+    deduped_3_1 := deduped_4_1 * deduped_5_1;
+    hoisted_2_1 := deduped_4_1;
+    hoisted_1_1 := deduped_5_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                    local deduped_1_2;
+                    deduped_1_2 := i_2 - 1;
+                    return REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1;
+                end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddCoevaluationMorphismWithGivenRange( cat,
+        
+########
+function ( cat_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1;
+    deduped_13_1 := UnderlyingMatrix( a_1 );
+    deduped_12_1 := UnderlyingRing( cat_1 );
+    deduped_11_1 := UnderlyingMatrix( b_1 );
+    deduped_10_1 := NumberColumns( deduped_13_1 );
+    deduped_9_1 := NumberColumns( deduped_11_1 );
+    deduped_8_1 := deduped_10_1 * deduped_9_1;
+    deduped_7_1 := deduped_9_1 * deduped_10_1;
+    deduped_6_1 := deduped_9_1 * deduped_9_1;
+    deduped_5_1 := HomalgIdentityMatrix( deduped_10_1, deduped_12_1 );
+    deduped_4_1 := HomalgIdentityMatrix( deduped_9_1, deduped_12_1 );
+    deduped_3_1 := UnionOfRows( deduped_12_1, deduped_8_1, [ KroneckerMat( deduped_13_1, deduped_4_1 ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_10_1, deduped_11_1 ) ) ] );
+    hoisted_2_1 := deduped_10_1;
+    hoisted_1_1 := deduped_9_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, r_1, UnderlyingMatrix, RightDivide( KroneckerMat( ConvertMatrixToRow( deduped_4_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_1_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_12_1 ), deduped_5_1 ) * DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_1_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_12_1 ) ) ), RightDivide( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_11_1 ), HomalgIdentityMatrix( deduped_8_1, deduped_12_1 ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( NumberRows( deduped_11_1 ), deduped_3_1 ) ) ), HomalgIdentityMatrix( deduped_9_1 * deduped_8_1, deduped_12_1 ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, deduped_3_1 ) ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, ReducedBasisOfRowModule( deduped_3_1 ) ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddEvaluationMorphismWithGivenSource( cat,
+        
+########
+function ( cat_1, a_1, b_1, s_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1;
+    deduped_14_1 := UnderlyingRing( cat_1 );
+    deduped_13_1 := UnderlyingMatrix( b_1 );
+    deduped_12_1 := UnderlyingMatrix( a_1 );
+    deduped_11_1 := NumberColumns( deduped_12_1 );
+    deduped_10_1 := NumberRows( deduped_12_1 );
+    deduped_9_1 := NumberColumns( deduped_13_1 );
+    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_14_1 );
+    deduped_7_1 := deduped_11_1 * deduped_9_1;
+    deduped_6_1 := DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_11_1, ReducedBasisOfRowModule( deduped_13_1 ) ) );
+    deduped_5_1 := deduped_7_1 * deduped_11_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_5_1, deduped_14_1 );
+    deduped_3_1 := Sum( [ NumberRows( deduped_6_1 ) * deduped_11_1, deduped_7_1 * deduped_10_1 ] ) + 1;
+    hoisted_2_1 := deduped_11_1;
+    hoisted_1_1 := deduped_9_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, b_1, UnderlyingMatrix, KroneckerMat( RightDivide( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_12_1 ), HomalgIdentityMatrix( deduped_9_1, deduped_14_1 ) ), DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_10_1, deduped_13_1 ) ) ), HomalgIdentityMatrix( deduped_7_1, deduped_14_1 ), DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_11_1, deduped_13_1 ) ) ), deduped_8_1 ) * (CertainColumns( RightDivide( deduped_4_1, UnionOfRows( deduped_14_1, deduped_5_1, [ UnionOfRows( deduped_14_1, deduped_5_1, [ KroneckerMat( deduped_6_1, deduped_8_1 ), DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_7_1, deduped_12_1 ) ) ] ), deduped_4_1 ] ) ), [ deduped_3_1 .. (deduped_3_1 - 1 + deduped_5_1) ] ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_14_1 ), deduped_8_1 ) * DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_9_1, ConvertMatrixToColumn( deduped_8_1 ) ) ))) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnMorphismsWithGivenInternalHoms( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := UnderlyingMatrix( Range( beta_1 ) );
+    deduped_3_1 := UnderlyingMatrix( Source( alpha_1 ) );
+    deduped_2_1 := UnderlyingMatrix( Source( beta_1 ) );
+    deduped_1_1 := UnderlyingMatrix( Range( alpha_1 ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, RightDivide( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberColumns( deduped_2_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ) * KroneckerMat( TransposedMatrix( UnderlyingMatrix( alpha_1 ) ), UnderlyingMatrix( beta_1 ) ), ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_3_1 ), HomalgIdentityMatrix( NumberColumns( deduped_4_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberRows( deduped_3_1 ), deduped_4_1 ) ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberColumns( deduped_3_1 ), deduped_4_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnObjects( cat,
+        
+########
+function ( cat_1, a_1, b_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1;
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := UnderlyingMatrix( b_1 );
+    deduped_1_1 := UnderlyingMatrix( a_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfRows( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberColumns( deduped_2_1 ), deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberColumns( deduped_1_1 ), deduped_2_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLeftUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddMultiplyWithElementOfCommutativeRingForMorphisms( cat,
         
@@ -234,6 +438,56 @@ end
         
     , 100 );
     
+    ##
+    AddRightUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnMorphismsWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, KroneckerMat( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( beta_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingMatrix( arg3_1 );
+    deduped_4_1 := UnderlyingMatrix( arg2_1 );
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := NumberColumns( deduped_5_1 );
+    deduped_1_1 := NumberColumns( deduped_4_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, UnionOfRows( deduped_3_1, deduped_1_1 * deduped_2_1, [ KroneckerMat( deduped_4_1, HomalgIdentityMatrix( deduped_2_1, deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( deduped_1_1, deduped_5_1 ) ) ] ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorUnit( cat,
+        
+########
+function ( cat_1 )
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, HomalgZeroMatrix( 0, 1, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     if IsBound( cat!.precompiled_functions_added ) then
         
         # COVERAGE_IGNORE_NEXT_LINE
diff --git a/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfFieldPrecompiled.gi b/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfFieldPrecompiled.gi
index fae4a6ef4c..385b7f5214 100644
--- a/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfFieldPrecompiled.gi
+++ b/ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfFieldPrecompiled.gi
@@ -129,6 +129,25 @@ end
         
     , 100 );
     
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) and NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
         
@@ -140,6 +159,42 @@ end
         
     , 100 );
     
+    ##
+    AddKernelEmbedding( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := Source( alpha_1 );
+    deduped_1_1 := ReducedSyzygiesOfRows( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( Range( alpha_1 ) ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfRows( deduped_1_1, UnderlyingMatrix( deduped_2_1 ) ) ), deduped_2_1, UnderlyingMatrix, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLiftAlongMonomorphism( cat,
+        
+########
+function ( cat_1, iota_1, tau_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( tau_1 ), Source( iota_1 ), UnderlyingMatrix, RightDivide( UnderlyingMatrix( tau_1 ), UnderlyingMatrix( iota_1 ), UnderlyingMatrix( Range( iota_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( alpha_1 ) * UnderlyingMatrix( beta_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
         
@@ -223,6 +278,155 @@ end
         
     , 100 );
     
+    ##
+    AddAssociatorLeftToRightWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddAssociatorRightToLeftWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddBraidingWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := NumberColumns( UnderlyingMatrix( b_1 ) );
+    deduped_4_1 := NumberColumns( UnderlyingMatrix( a_1 ) );
+    deduped_3_1 := deduped_4_1 * deduped_5_1;
+    hoisted_2_1 := deduped_4_1;
+    hoisted_1_1 := deduped_5_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                    local deduped_1_2;
+                    deduped_1_2 := i_2 - 1;
+                    return REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1;
+                end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddCoevaluationMorphismWithGivenRange( cat,
+        
+########
+function ( cat_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1;
+    deduped_13_1 := UnderlyingMatrix( a_1 );
+    deduped_12_1 := UnderlyingRing( cat_1 );
+    deduped_11_1 := UnderlyingMatrix( b_1 );
+    deduped_10_1 := NumberColumns( deduped_13_1 );
+    deduped_9_1 := NumberColumns( deduped_11_1 );
+    deduped_8_1 := deduped_10_1 * deduped_9_1;
+    deduped_7_1 := deduped_9_1 * deduped_10_1;
+    deduped_6_1 := deduped_9_1 * deduped_9_1;
+    deduped_5_1 := HomalgIdentityMatrix( deduped_10_1, deduped_12_1 );
+    deduped_4_1 := HomalgIdentityMatrix( deduped_9_1, deduped_12_1 );
+    deduped_3_1 := UnionOfRows( deduped_12_1, deduped_8_1, [ KroneckerMat( deduped_13_1, deduped_4_1 ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_10_1, deduped_11_1 ) ) ] );
+    hoisted_2_1 := deduped_10_1;
+    hoisted_1_1 := deduped_9_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, r_1, UnderlyingMatrix, RightDivide( KroneckerMat( ConvertMatrixToRow( deduped_4_1 ), deduped_5_1 ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_1_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_12_1 ), deduped_5_1 ) * DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_2_1 ) * hoisted_1_1 + QUO_INT( deduped_1_2, hoisted_2_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_12_1 ) ) ), RightDivide( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_11_1 ), HomalgIdentityMatrix( deduped_8_1, deduped_12_1 ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( NumberRows( deduped_11_1 ), deduped_3_1 ) ) ), HomalgIdentityMatrix( deduped_9_1 * deduped_8_1, deduped_12_1 ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, deduped_3_1 ) ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, ReducedBasisOfRowModule( deduped_3_1 ) ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddEvaluationMorphismWithGivenSource( cat,
+        
+########
+function ( cat_1, a_1, b_1, s_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1;
+    deduped_14_1 := UnderlyingRing( cat_1 );
+    deduped_13_1 := UnderlyingMatrix( b_1 );
+    deduped_12_1 := UnderlyingMatrix( a_1 );
+    deduped_11_1 := NumberColumns( deduped_12_1 );
+    deduped_10_1 := NumberRows( deduped_12_1 );
+    deduped_9_1 := NumberColumns( deduped_13_1 );
+    deduped_8_1 := HomalgIdentityMatrix( deduped_11_1, deduped_14_1 );
+    deduped_7_1 := deduped_11_1 * deduped_9_1;
+    deduped_6_1 := DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_11_1, ReducedBasisOfRowModule( deduped_13_1 ) ) );
+    deduped_5_1 := deduped_7_1 * deduped_11_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_5_1, deduped_14_1 );
+    deduped_3_1 := Sum( [ NumberRows( deduped_6_1 ) * deduped_11_1, deduped_7_1 * deduped_10_1 ] ) + 1;
+    hoisted_2_1 := deduped_11_1;
+    hoisted_1_1 := deduped_9_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, b_1, UnderlyingMatrix, KroneckerMat( RightDivide( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_12_1 ), HomalgIdentityMatrix( deduped_9_1, deduped_14_1 ) ), DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_10_1, deduped_13_1 ) ) ), HomalgIdentityMatrix( deduped_7_1, deduped_14_1 ), DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_11_1, deduped_13_1 ) ) ), deduped_8_1 ) * (CertainColumns( RightDivide( deduped_4_1, UnionOfRows( deduped_14_1, deduped_5_1, [ UnionOfRows( deduped_14_1, deduped_5_1, [ KroneckerMat( deduped_6_1, deduped_8_1 ), DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_7_1, deduped_12_1 ) ) ] ), deduped_4_1 ] ) ), [ deduped_3_1 .. (deduped_3_1 - 1 + deduped_5_1) ] ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_14_1 ), deduped_8_1 ) * DiagMat( deduped_14_1, ListWithIdenticalEntries( deduped_9_1, ConvertMatrixToColumn( deduped_8_1 ) ) ))) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnMorphismsWithGivenInternalHoms( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := UnderlyingMatrix( Range( beta_1 ) );
+    deduped_3_1 := UnderlyingMatrix( Source( alpha_1 ) );
+    deduped_2_1 := UnderlyingMatrix( Source( beta_1 ) );
+    deduped_1_1 := UnderlyingMatrix( Range( alpha_1 ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, RightDivide( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberColumns( deduped_2_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ) * KroneckerMat( TransposedMatrix( UnderlyingMatrix( alpha_1 ) ), UnderlyingMatrix( beta_1 ) ), ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_3_1 ), HomalgIdentityMatrix( NumberColumns( deduped_4_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberRows( deduped_3_1 ), deduped_4_1 ) ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberColumns( deduped_3_1 ), deduped_4_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnObjects( cat,
+        
+########
+function ( cat_1, a_1, b_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1;
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := UnderlyingMatrix( b_1 );
+    deduped_1_1 := UnderlyingMatrix( a_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfRows( ReducedSyzygiesOfRows( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberColumns( deduped_2_1 ), deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberColumns( deduped_1_1 ), deduped_2_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLeftUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddMultiplyWithElementOfCommutativeRingForMorphisms( cat,
         
@@ -234,6 +438,56 @@ end
         
     , 100 );
     
+    ##
+    AddRightUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberColumns( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnMorphismsWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, KroneckerMat( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( beta_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingMatrix( arg3_1 );
+    deduped_4_1 := UnderlyingMatrix( arg2_1 );
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := NumberColumns( deduped_5_1 );
+    deduped_1_1 := NumberColumns( deduped_4_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, UnionOfRows( deduped_3_1, deduped_1_1 * deduped_2_1, [ KroneckerMat( deduped_4_1, HomalgIdentityMatrix( deduped_2_1, deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( deduped_1_1, deduped_5_1 ) ) ] ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorUnit( cat,
+        
+########
+function ( cat_1 )
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, HomalgZeroMatrix( 0, 1, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     if IsBound( cat!.precompiled_functions_added ) then
         
         # COVERAGE_IGNORE_NEXT_LINE
diff --git a/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfArbitraryRingPrecompiled.gi b/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfArbitraryRingPrecompiled.gi
index d68fad3743..9caa4b418e 100644
--- a/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfArbitraryRingPrecompiled.gi
+++ b/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfArbitraryRingPrecompiled.gi
@@ -129,6 +129,25 @@ end
         
     , 100 );
     
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) and NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
         
@@ -140,6 +159,42 @@ end
         
     , 100 );
     
+    ##
+    AddKernelEmbedding( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := Source( alpha_1 );
+    deduped_1_1 := ReducedSyzygiesOfColumns( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( Range( alpha_1 ) ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfColumns( deduped_1_1, UnderlyingMatrix( deduped_2_1 ) ) ), deduped_2_1, UnderlyingMatrix, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLiftAlongMonomorphism( cat,
+        
+########
+function ( cat_1, iota_1, tau_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( tau_1 ), Source( iota_1 ), UnderlyingMatrix, LeftDivide( UnderlyingMatrix( iota_1 ), UnderlyingMatrix( tau_1 ), UnderlyingMatrix( Range( iota_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( beta_1 ) * UnderlyingMatrix( alpha_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
         
diff --git a/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfCommutativeRingPrecompiled.gi b/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfCommutativeRingPrecompiled.gi
index 8f052556ec..c07e58e593 100644
--- a/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfCommutativeRingPrecompiled.gi
+++ b/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfCommutativeRingPrecompiled.gi
@@ -129,6 +129,25 @@ end
         
     , 100 );
     
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) and NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
         
@@ -140,6 +159,42 @@ end
         
     , 100 );
     
+    ##
+    AddKernelEmbedding( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := Source( alpha_1 );
+    deduped_1_1 := ReducedSyzygiesOfColumns( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( Range( alpha_1 ) ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfColumns( deduped_1_1, UnderlyingMatrix( deduped_2_1 ) ) ), deduped_2_1, UnderlyingMatrix, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLiftAlongMonomorphism( cat,
+        
+########
+function ( cat_1, iota_1, tau_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( tau_1 ), Source( iota_1 ), UnderlyingMatrix, LeftDivide( UnderlyingMatrix( iota_1 ), UnderlyingMatrix( tau_1 ), UnderlyingMatrix( Range( iota_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( beta_1 ) * UnderlyingMatrix( alpha_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
         
@@ -223,6 +278,155 @@ end
         
     , 100 );
     
+    ##
+    AddAssociatorLeftToRightWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddAssociatorRightToLeftWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddBraidingWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := NumberRows( UnderlyingMatrix( b_1 ) );
+    deduped_4_1 := NumberRows( UnderlyingMatrix( a_1 ) );
+    deduped_3_1 := deduped_4_1 * deduped_5_1;
+    hoisted_2_1 := deduped_5_1;
+    hoisted_1_1 := deduped_4_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                    local deduped_1_2;
+                    deduped_1_2 := i_2 - 1;
+                    return REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1;
+                end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddCoevaluationMorphismWithGivenRange( cat,
+        
+########
+function ( cat_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1;
+    deduped_13_1 := UnderlyingRing( cat_1 );
+    deduped_12_1 := UnderlyingMatrix( a_1 );
+    deduped_11_1 := UnderlyingMatrix( b_1 );
+    deduped_10_1 := NumberRows( deduped_12_1 );
+    deduped_9_1 := NumberRows( deduped_11_1 );
+    deduped_8_1 := HomalgIdentityMatrix( deduped_10_1, deduped_13_1 );
+    deduped_7_1 := deduped_9_1 * deduped_9_1;
+    deduped_6_1 := deduped_9_1 * deduped_10_1;
+    deduped_5_1 := HomalgIdentityMatrix( deduped_9_1, deduped_13_1 );
+    deduped_4_1 := deduped_10_1 * deduped_9_1;
+    deduped_3_1 := UnionOfColumns( deduped_13_1, deduped_4_1, [ KroneckerMat( deduped_12_1, deduped_5_1 ), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_10_1, deduped_11_1 ) ) ] );
+    hoisted_2_1 := deduped_10_1;
+    hoisted_1_1 := deduped_9_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, r_1, UnderlyingMatrix, LeftDivide( LeftDivide( HomalgIdentityMatrix( deduped_9_1 * deduped_4_1, deduped_13_1 ), ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_11_1 ), HomalgIdentityMatrix( deduped_4_1, deduped_13_1 ) ), DiagMat( deduped_13_1, ListWithIdenticalEntries( NumberColumns( deduped_11_1 ), deduped_3_1 ) ) ), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_9_1, deduped_3_1 ) ) ), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_13_1 ) ) ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_1_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_13_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_5_1 ), deduped_8_1 )), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_9_1, ReducedBasisOfColumnModule( deduped_3_1 ) ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddEvaluationMorphismWithGivenSource( cat,
+        
+########
+function ( cat_1, a_1, b_1, s_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1;
+    deduped_14_1 := UnderlyingMatrix( a_1 );
+    deduped_13_1 := UnderlyingMatrix( b_1 );
+    deduped_12_1 := UnderlyingRing( cat_1 );
+    deduped_11_1 := NumberColumns( deduped_14_1 );
+    deduped_10_1 := NumberRows( deduped_14_1 );
+    deduped_9_1 := NumberRows( deduped_13_1 );
+    deduped_8_1 := deduped_10_1 * deduped_9_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_12_1 );
+    deduped_6_1 := DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_10_1, ReducedBasisOfColumnModule( deduped_13_1 ) ) );
+    deduped_5_1 := deduped_8_1 * deduped_10_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_5_1, deduped_12_1 );
+    deduped_3_1 := Sum( [ NumberColumns( deduped_6_1 ) * deduped_10_1, deduped_8_1 * deduped_11_1 ] ) + 1;
+    hoisted_2_1 := deduped_9_1;
+    hoisted_1_1 := deduped_10_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, b_1, UnderlyingMatrix, DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, ConvertMatrixToRow( deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_12_1 ), deduped_7_1 ) * CertainRows( LeftDivide( UnionOfColumns( deduped_12_1, deduped_5_1, [ UnionOfColumns( deduped_12_1, deduped_5_1, [ KroneckerMat( deduped_6_1, deduped_7_1 ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_8_1, deduped_14_1 ) ) ] ), deduped_4_1 ] ), deduped_4_1 ), [ deduped_3_1 .. (deduped_3_1 - 1 + deduped_5_1) ] ) * KroneckerMat( LeftDivide( HomalgIdentityMatrix( deduped_8_1, deduped_12_1 ), ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_14_1 ), HomalgIdentityMatrix( deduped_9_1, deduped_12_1 ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_11_1, deduped_13_1 ) ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_10_1, deduped_13_1 ) ) ), deduped_7_1 ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnMorphismsWithGivenInternalHoms( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := UnderlyingMatrix( Source( beta_1 ) );
+    deduped_3_1 := UnderlyingMatrix( Range( alpha_1 ) );
+    deduped_2_1 := UnderlyingMatrix( Range( beta_1 ) );
+    deduped_1_1 := UnderlyingMatrix( Source( alpha_1 ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, LeftDivide( ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberRows( deduped_2_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberColumns( deduped_1_1 ), deduped_2_1 ) ) ), KroneckerMat( TransposedMatrix( UnderlyingMatrix( alpha_1 ) ), UnderlyingMatrix( beta_1 ) ) * ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_3_1 ), HomalgIdentityMatrix( NumberRows( deduped_4_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberColumns( deduped_3_1 ), deduped_4_1 ) ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnObjects( cat,
+        
+########
+function ( cat_1, a_1, b_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1;
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := UnderlyingMatrix( b_1 );
+    deduped_1_1 := UnderlyingMatrix( a_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfColumns( ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberRows( deduped_2_1 ), deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberColumns( deduped_1_1 ), deduped_2_1 ) ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLeftUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddMultiplyWithElementOfCommutativeRingForMorphisms( cat,
         
@@ -234,6 +438,56 @@ end
         
     , 100 );
     
+    ##
+    AddRightUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnMorphismsWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, KroneckerMat( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( beta_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingMatrix( arg3_1 );
+    deduped_4_1 := UnderlyingMatrix( arg2_1 );
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := NumberRows( deduped_5_1 );
+    deduped_1_1 := NumberRows( deduped_4_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, UnionOfColumns( deduped_3_1, deduped_1_1 * deduped_2_1, [ KroneckerMat( deduped_4_1, HomalgIdentityMatrix( deduped_2_1, deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( deduped_1_1, deduped_5_1 ) ) ] ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorUnit( cat,
+        
+########
+function ( cat_1 )
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, HomalgZeroMatrix( 1, 0, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     if IsBound( cat!.precompiled_functions_added ) then
         
         # COVERAGE_IGNORE_NEXT_LINE
diff --git a/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfFieldPrecompiled.gi b/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfFieldPrecompiled.gi
index cdff8fad44..eec97e826b 100644
--- a/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfFieldPrecompiled.gi
+++ b/ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfFieldPrecompiled.gi
@@ -129,6 +129,25 @@ end
         
     , 100 );
     
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) and NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
         
@@ -140,6 +159,42 @@ end
         
     , 100 );
     
+    ##
+    AddKernelEmbedding( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := Source( alpha_1 );
+    deduped_1_1 := ReducedSyzygiesOfColumns( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( Range( alpha_1 ) ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfColumns( deduped_1_1, UnderlyingMatrix( deduped_2_1 ) ) ), deduped_2_1, UnderlyingMatrix, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLiftAlongMonomorphism( cat,
+        
+########
+function ( cat_1, iota_1, tau_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( tau_1 ), Source( iota_1 ), UnderlyingMatrix, LeftDivide( UnderlyingMatrix( iota_1 ), UnderlyingMatrix( tau_1 ), UnderlyingMatrix( Range( iota_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( beta_1 ) * UnderlyingMatrix( alpha_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
         
@@ -223,6 +278,155 @@ end
         
     , 100 );
     
+    ##
+    AddAssociatorLeftToRightWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddAssociatorRightToLeftWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, c_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( s_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddBraidingWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := NumberRows( UnderlyingMatrix( b_1 ) );
+    deduped_4_1 := NumberRows( UnderlyingMatrix( a_1 ) );
+    deduped_3_1 := deduped_4_1 * deduped_5_1;
+    hoisted_2_1 := deduped_5_1;
+    hoisted_1_1 := deduped_4_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_3_1 ], function ( i_2 )
+                    local deduped_1_2;
+                    deduped_1_2 := i_2 - 1;
+                    return REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1;
+                end ) ), deduped_3_1 ), deduped_3_1, deduped_3_1, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddCoevaluationMorphismWithGivenRange( cat,
+        
+########
+function ( cat_1, a_1, b_1, r_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1;
+    deduped_13_1 := UnderlyingRing( cat_1 );
+    deduped_12_1 := UnderlyingMatrix( a_1 );
+    deduped_11_1 := UnderlyingMatrix( b_1 );
+    deduped_10_1 := NumberRows( deduped_12_1 );
+    deduped_9_1 := NumberRows( deduped_11_1 );
+    deduped_8_1 := HomalgIdentityMatrix( deduped_10_1, deduped_13_1 );
+    deduped_7_1 := deduped_9_1 * deduped_9_1;
+    deduped_6_1 := deduped_9_1 * deduped_10_1;
+    deduped_5_1 := HomalgIdentityMatrix( deduped_9_1, deduped_13_1 );
+    deduped_4_1 := deduped_10_1 * deduped_9_1;
+    deduped_3_1 := UnionOfColumns( deduped_13_1, deduped_4_1, [ KroneckerMat( deduped_12_1, deduped_5_1 ), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_10_1, deduped_11_1 ) ) ] );
+    hoisted_2_1 := deduped_10_1;
+    hoisted_1_1 := deduped_9_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, a_1, r_1, UnderlyingMatrix, LeftDivide( LeftDivide( HomalgIdentityMatrix( deduped_9_1 * deduped_4_1, deduped_13_1 ), ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_11_1 ), HomalgIdentityMatrix( deduped_4_1, deduped_13_1 ) ), DiagMat( deduped_13_1, ListWithIdenticalEntries( NumberColumns( deduped_11_1 ), deduped_3_1 ) ) ), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_9_1, deduped_3_1 ) ) ), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_9_1, HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_6_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_6_1 ), deduped_6_1, deduped_6_1, deduped_13_1 ) ) ) * (KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_7_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_1_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_7_1 ), deduped_7_1, deduped_7_1, deduped_13_1 ), deduped_8_1 ) * KroneckerMat( ConvertMatrixToColumn( deduped_5_1 ), deduped_8_1 )), DiagMat( deduped_13_1, ListWithIdenticalEntries( deduped_9_1, ReducedBasisOfColumnModule( deduped_3_1 ) ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddEvaluationMorphismWithGivenSource( cat,
+        
+########
+function ( cat_1, a_1, b_1, s_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1, deduped_4_1, deduped_5_1, deduped_6_1, deduped_7_1, deduped_8_1, deduped_9_1, deduped_10_1, deduped_11_1, deduped_12_1, deduped_13_1, deduped_14_1;
+    deduped_14_1 := UnderlyingMatrix( a_1 );
+    deduped_13_1 := UnderlyingMatrix( b_1 );
+    deduped_12_1 := UnderlyingRing( cat_1 );
+    deduped_11_1 := NumberColumns( deduped_14_1 );
+    deduped_10_1 := NumberRows( deduped_14_1 );
+    deduped_9_1 := NumberRows( deduped_13_1 );
+    deduped_8_1 := deduped_10_1 * deduped_9_1;
+    deduped_7_1 := HomalgIdentityMatrix( deduped_10_1, deduped_12_1 );
+    deduped_6_1 := DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_10_1, ReducedBasisOfColumnModule( deduped_13_1 ) ) );
+    deduped_5_1 := deduped_8_1 * deduped_10_1;
+    deduped_4_1 := HomalgIdentityMatrix( deduped_5_1, deduped_12_1 );
+    deduped_3_1 := Sum( [ NumberColumns( deduped_6_1 ) * deduped_10_1, deduped_8_1 * deduped_11_1 ] ) + 1;
+    hoisted_2_1 := deduped_9_1;
+    hoisted_1_1 := deduped_10_1;
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, b_1, UnderlyingMatrix, DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_9_1, ConvertMatrixToRow( deduped_7_1 ) ) ) * KroneckerMat( HomalgMatrix( PermutationMat( PermList( List( [ 1 .. deduped_8_1 ], function ( i_2 )
+                            local deduped_1_2;
+                            deduped_1_2 := (i_2 - 1);
+                            return (REM_INT( deduped_1_2, hoisted_1_1 ) * hoisted_2_1 + QUO_INT( deduped_1_2, hoisted_1_1 ) + 1);
+                        end ) ), deduped_8_1 ), deduped_8_1, deduped_8_1, deduped_12_1 ), deduped_7_1 ) * CertainRows( LeftDivide( UnionOfColumns( deduped_12_1, deduped_5_1, [ UnionOfColumns( deduped_12_1, deduped_5_1, [ KroneckerMat( deduped_6_1, deduped_7_1 ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_8_1, deduped_14_1 ) ) ] ), deduped_4_1 ] ), deduped_4_1 ), [ deduped_3_1 .. (deduped_3_1 - 1 + deduped_5_1) ] ) * KroneckerMat( LeftDivide( HomalgIdentityMatrix( deduped_8_1, deduped_12_1 ), ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_14_1 ), HomalgIdentityMatrix( deduped_9_1, deduped_12_1 ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_11_1, deduped_13_1 ) ) ), DiagMat( deduped_12_1, ListWithIdenticalEntries( deduped_10_1, deduped_13_1 ) ) ), deduped_7_1 ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnMorphismsWithGivenInternalHoms( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingRing( cat_1 );
+    deduped_4_1 := UnderlyingMatrix( Source( beta_1 ) );
+    deduped_3_1 := UnderlyingMatrix( Range( alpha_1 ) );
+    deduped_2_1 := UnderlyingMatrix( Range( beta_1 ) );
+    deduped_1_1 := UnderlyingMatrix( Source( alpha_1 ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, LeftDivide( ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberRows( deduped_2_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberColumns( deduped_1_1 ), deduped_2_1 ) ) ), KroneckerMat( TransposedMatrix( UnderlyingMatrix( alpha_1 ) ), UnderlyingMatrix( beta_1 ) ) * ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_3_1 ), HomalgIdentityMatrix( NumberRows( deduped_4_1 ), deduped_5_1 ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberColumns( deduped_3_1 ), deduped_4_1 ) ) ), DiagMat( deduped_5_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddInternalHomOnObjects( cat,
+        
+########
+function ( cat_1, a_1, b_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1;
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := UnderlyingMatrix( b_1 );
+    deduped_1_1 := UnderlyingMatrix( a_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, ReducedSyzygiesOfColumns( ReducedSyzygiesOfColumns( KroneckerMat( TransposedMatrix( deduped_1_1 ), HomalgIdentityMatrix( NumberRows( deduped_2_1 ), deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberColumns( deduped_1_1 ), deduped_2_1 ) ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( NumberRows( deduped_1_1 ), deduped_2_1 ) ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddLeftUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddMultiplyWithElementOfCommutativeRingForMorphisms( cat,
         
@@ -234,6 +438,56 @@ end
         
     , 100 );
     
+    ##
+    AddRightUnitorWithGivenTensorProduct( cat,
+        
+########
+function ( cat_1, a_1, s_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, a_1, UnderlyingMatrix, HomalgIdentityMatrix( NumberRows( UnderlyingMatrix( a_1 ) ), UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnMorphismsWithGivenTensorProducts( cat,
+        
+########
+function ( cat_1, s_1, alpha_1, beta_1, r_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, UnderlyingMatrix, KroneckerMat( UnderlyingMatrix( alpha_1 ), UnderlyingMatrix( beta_1 ) ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorProductOnObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := UnderlyingMatrix( arg3_1 );
+    deduped_4_1 := UnderlyingMatrix( arg2_1 );
+    deduped_3_1 := UnderlyingRing( cat_1 );
+    deduped_2_1 := NumberRows( deduped_5_1 );
+    deduped_1_1 := NumberRows( deduped_4_1 );
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, UnionOfColumns( deduped_3_1, deduped_1_1 * deduped_2_1, [ KroneckerMat( deduped_4_1, HomalgIdentityMatrix( deduped_2_1, deduped_3_1 ) ), DiagMat( deduped_3_1, ListWithIdenticalEntries( deduped_1_1, deduped_5_1 ) ) ] ) );
+end
+########
+        
+    , 100 );
+    
+    ##
+    AddTensorUnit( cat,
+        
+########
+function ( cat_1 )
+    return CreateCapCategoryObjectWithAttributes( cat_1, UnderlyingMatrix, HomalgZeroMatrix( 1, 0, UnderlyingRing( cat_1 ) ) );
+end
+########
+        
+    , 100 );
+    
     if IsBound( cat!.precompiled_functions_added ) then
         
         # COVERAGE_IGNORE_NEXT_LINE