diff --git a/PackageInfo.g b/PackageInfo.g
index 9ec29d4..99c7f45 100644
--- a/PackageInfo.g
+++ b/PackageInfo.g
@@ -11,7 +11,7 @@ SetPackageInfo( rec(
PackageName := "CatReps",
Subtitle := "Representations and cohomology of finite categories",
Version := Maximum( [
- "2020.04.07", ## Mohamed's version
+ "2020.04.08", ## Mohamed's version
## this line prevents merge conflicts
"2020.01.01", ## Tibor's version
## this line prevents merge conflicts
@@ -111,7 +111,7 @@ Dependencies := rec(
[ "SubcategoriesForCAP", ">= 2020.02.02" ],
[ "MatricesForHomalg", ">= 2020.02.02" ],
[ "Toposes", ">= 2020.02.19" ],
- [ "FunctorCategories", ">= 2020.04.07" ],
+ [ "FunctorCategories", ">= 2020.04.08" ],
],
SuggestedOtherPackages := [ ],
ExternalConditions := [ ],
diff --git a/doc/Doc.autodoc b/doc/Doc.autodoc
index 191273c..9490004 100644
--- a/doc/Doc.autodoc
+++ b/doc/Doc.autodoc
@@ -4,4 +4,8 @@
@Section Global variables
@Section Attributes
@Section Constructors
+@Section Operations
@Section Tools
+@Section Example
+
+@InsertChunk CategoryOfRepresentations
diff --git a/examples/CategoryOfRepresentations.g b/examples/CategoryOfRepresentations.g
index bfce9ed..bd026de 100644
--- a/examples/CategoryOfRepresentations.g
+++ b/examples/CategoryOfRepresentations.g
@@ -14,6 +14,7 @@ GF3q := PathAlgebra( GF3, qc3c3 );
rel := [GF3q.a^3-GF3q.1, GF3q.c^3-GF3q.2, GF3q.a*GF3q.b-GF3q.b*GF3q.c];;
kq := Algebroid( GF3q, rel );
#! Algebroid generated by the right quiver q(2)[a:1->1,b:1->2,c:2->2]
+SetIsLinearClosureOfACategory( kq, true );
#! @EndExample
#! A representation of the category c3c3 is another way to encode
@@ -25,49 +26,14 @@ kq := Algebroid( GF3q, rel );
#! The above relation of the quiver states that the value of (b) is
#! a module homomorphism from the first to the second $C_3$-module.
-#! Now we add the bialgebroid structure:
-
-#! @Example
-counit := rec( a := 1, b := 1, c := 1 );
-#! rec( a := 1, b := 1, c := 1 )
-kq2 := kq^2;
-#! Algebroid generated by the right quiver qxq(1x1,1x2,2x1,2x2)\
-#! [1xa:1x1->1x1,1xb:1x1->1x2,1xc:1x2->1x2,2xa:2x1->2x1,2xb:2x1->2x2,2xc:2x2->2x2,\
-#! ax1:1x1->1x1,ax2:1x2->1x2,bx1:1x1->2x1,bx2:1x2->2x2,cx1:2x1->2x1,cx2:2x2->2x2]
-PreCompose( kq2.ax1, kq2.1xa ) = PreCompose( kq2.1xa, kq2.ax1 );
-#! true
-PreCompose( kq2.bx1, kq2.2xb ) = PreCompose( kq2.1xb, kq2.bx2 );
-#! true
-PreCompose( kq2.cx2, kq2.2xc ) = PreCompose( kq2.2xc, kq2.cx2 );
-#! true
-comult := rec( a := PreCompose( kq2.ax1, kq2.1xa ),
- b := PreCompose( kq2.1xb, kq2.bx2 ),
- c := PreCompose( kq2.cx2, kq2.2xc ) );
-#! rec( a := (1x1)-[{ Z(3)^0*(1xa*ax1) }]->(1x1),
-#! b := (1x1)-[{ Z(3)^0*(1xb*bx2) }]->(2x2),
-#! c := (2x2)-[{ Z(3)^0*(2xc*cx2) }]->(2x2) )
-AddBialgebroidStructure( kq, counit, comult );
-#! Bialgebroid generated by the right quiver q(2)[a:1->1,b:1->2,c:2->2]
-counit := Counit( kq );
-#! Functor from finitely presented Bialgebroid generated by
-#! the right quiver q(2)[a:1->1,b:1->2,c:2->2] ->
-#! Algebra generated by the right quiver *(1)[]
-comult := Comultiplication( kq );
-#! Functor from finitely presented Bialgebroid generated by
-#! the right quiver q(2)[a:1->1,b:1->2,c:2->2] ->
-#! Algebroid generated by the right quiver qxq(1x1,1x2,2x1,2x2)
-#! [1xa:1x1->1x1,1xb:1x1->1x2,1xc:1x2->1x2,2xa:2x1->2x1,2xb:2x1->2x2,2xc:2x2->2x2,\
-#! ax1:1x1->1x1,ax2:1x2->1x2,bx1:1x1->2x1,bx2:1x2->2x2,cx1:2x1->2x1,cx2:2x2->2x2]
-#! @EndExample
-
#! @Example
kmat := MatrixCategory( GF3 );
#! Category of matrices over GF(3)
-CatReps := CategoryOfRepresentations( kq, kmat );
-#! The category of functors: Bialgebroid generated by the right quiver
+CatReps := Hom( kq, kmat );
+#! The category of functors: Algebroid generated by the right quiver
#! q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices over GF(3)
InfoOfInstalledOperationsOfCategory( CatReps );
-#! 109 primitive operations were used to derive 237 operations for this category which
+#! 108 primitive operations were used to derive 236 operations for this category which
#! * IsLinearCategoryOverCommutativeRing
#! * IsSymmetricMonoidalCategory
#! * IsAbelianCategory
@@ -76,7 +42,7 @@ CommutativeRingOfLinearCategory( CatReps );
zero := ZeroObject( CatReps );
#! <(1)->0, (2)->0; (a)->0x0, (b)->0x0, (c)->0x0>
Display( zero );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -106,7 +72,7 @@ Display( zero );
const := TensorUnit( CatReps );
#! <(1)->1, (2)->1; (a)->1x1, (b)->1x1, (c)->1x1>
Display( const );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -139,7 +105,7 @@ f := [[1,1,0,0],[0,1,1,0],[0,0,1,0],[0,0,0,1]];;
nine := AsObjectInHomCategory( kq, [ 5, 4 ], [ d, e, f ] );
#! <(1)->5, (2)->4; (a)->5x5, (b)->5x4, (c)->4x4>
Display( nine );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -208,7 +174,7 @@ fortyone(kq.b) = TensorProductOnMorphisms( nine(kq.b), nine(kq.b) );
fortyone(kq.c) = TensorProductOnMorphisms( nine(kq.c), nine(kq.c) );
#! true
Display( fortyone );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -310,7 +276,7 @@ IsIsomorphism( iso );
iso;
#! <(1)->25x25, (2)->16x16>
Display( Source( iso ) );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -401,7 +367,7 @@ Display( Source( iso ) );
#!
#! A morphism in Category of matrices over GF(3)
Display( iso );
-#! A morphism in The category of functors: Bialgebroid generated by the
+#! A morphism in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -462,7 +428,7 @@ TensorProductOnMorphisms( eta, eta );
six := Source( eta );
#! <(1)->3, (2)->3; (a)->3x3, (b)->3x3, (c)->3x3>
Display( six );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -498,7 +464,7 @@ Display( six );
emb := EmbeddingOfSumOfImagesOfAllMorphisms( const, six );
#! <(1)->1x3, (2)->0x3>
Display( emb );
-#! A morphism in The category of functors: Bialgebroid generated by the
+#! A morphism in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -506,7 +472,7 @@ Display( emb );
#! Image of <(1)>:
#! . . 1
#!
-#! A split monomorphism in Category of matrices over GF(3)
+#! A morphism in Category of matrices over GF(3)
#!
#!
#! Image of <(2)>:
@@ -516,7 +482,7 @@ Display( emb );
s1 := Source( emb );
#! <(1)->1, (2)->0; (a)->1x1, (b)->1x0, (c)->0x0>
Display( s1 );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -546,7 +512,7 @@ Display( s1 );
proj1 := YonedaProjective( CatReps, kq.1 );
#! <(1)->3, (2)->3; (a)->3x3, (b)->3x3, (c)->3x3>
Display( proj1 );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -588,7 +554,7 @@ IsEpimorphism( EmbeddingOfSumOfImagesOfAllMorphisms( proj1, six ) );
five := CokernelObject( emb );
#! <(1)->2, (2)->3; (a)->2x2, (b)->2x3, (c)->3x3>
Display( five );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
@@ -632,7 +598,7 @@ SumOfImagesOfAllMorphisms( six, const );
proj2 := YonedaProjective( CatReps, kq.2 );
#! <(1)->0, (2)->3; (a)->0x0, (b)->0x3, (c)->3x3>
Display( proj2 );
-#! An object in The category of functors: Bialgebroid generated by the
+#! An object in The category of functors: Algebroid generated by the
#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
#! over GF(3) defined by the following data:
#!
diff --git a/gap/CatRepsWithCAP.gd b/gap/CatRepsWithCAP.gd
index ae882c2..a7613a6 100644
--- a/gap/CatRepsWithCAP.gd
+++ b/gap/CatRepsWithCAP.gd
@@ -83,15 +83,6 @@ DeclareOperation( "ConcreteCategoryForCAP",
[ IsList ] );
#! @InsertChunk ConcreteCategoryForCAP
-#! @Description
-#! Construct the category of representations of the algebroid kq
-#! with values in the Abelian category A.
-#! @Arguments kq, A
-#! @Returns a &CAP; category
-DeclareOperation( "CategoryOfRepresentations",
- [ IsAlgebroid, IsCapCategory ] );
-#! @InsertChunk CategoryOfRepresentations
-
#! @Description
#! Concstruct the embedding of a subrepresentation $S$ of F
#! by a list eta of morphisms, where the image embeddings thereof are
diff --git a/gap/CatRepsWithCAP.gi b/gap/CatRepsWithCAP.gi
index 80c4ed3..1315a2b 100644
--- a/gap/CatRepsWithCAP.gi
+++ b/gap/CatRepsWithCAP.gi
@@ -56,50 +56,6 @@ InstallMethod( ConcreteCategoryForCAP,
end );
-##
-InstallMethod( CategoryOfRepresentations,
- "for an algebroid and a CAP category",
- [ IsAlgebroid, IsCapCategory ],
-
- function( kq, A )
- local CatReps;
-
- CatReps := Hom( kq, A :
- doctrines := [ [ "IsSymmetricMonoidalCategory", true ] ],
- FinalizeCategory := false );
-
- AddTensorUnit( CatReps,
- function( )
- local objects, morphisms;
-
- objects := List( [ 1 .. Length( SetOfObjects( kq ) ) ], i -> TensorUnit( A ) );
- morphisms := List( [ 1 .. Length( SetOfGeneratingMorphisms( kq ) ) ], i -> IdentityMorphism( TensorUnit( A ) ) );
-
- return AsObjectInHomCategory( kq, objects, morphisms );
-
- end );
-
- AddTensorProductOnObjects( CatReps,
- function( F, G )
- local objects, morphisms;
-
- objects := ListN( ValuesOnAllObjects( F ), ValuesOnAllObjects( G ), TensorProductOnObjects );
- morphisms := ListN( ValuesOnAllGeneratingMorphisms( F ), ValuesOnAllGeneratingMorphisms( G ), TensorProductOnMorphisms );
-
- return AsObjectInHomCategory( kq, objects, morphisms );
-
- end );
-
- if ValueOption( "FinalizeCategory" ) = false then
- return CatReps;
- fi;
-
- Finalize( CatReps );
-
- return CatReps;
-
-end );
-
##
InstallMethod( RecordOfCategory,
"for an algebroid",