make use of simpler input to create category representations

needs FunctorCategories v2020.04.07

PackageInfo.g

@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 PackageName := "CatReps",
 Subtitle := "Representations and cohomology of finite categories",
 Version := Maximum( [
-                   "2020.04.06", ## Mohamed's version
+                   "2020.04.07", ## 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", ">= 2020.04.04" ],
+                   [ "FunctorCategories", ">= 2020.04.07" ],
                    ],
   SuggestedOtherPackages := [ ],
   ExternalConditions := [ ],

examples/CategoryOfRepresentations.g

@@ -133,47 +133,50 @@ Display( const );
 #!  1
 #! 
 #! An identity morphism in Category of matrices over GF(3)
-V1 := VectorSpaceObject( 5, GF3 );
-#! <A vector space object over GF(3) of dimension 5>
-V2 := VectorSpaceObject( 4, GF3 );
-#! <A vector space object over GF(3) of dimension 4>
-d := One(GF3) * [[1,1,0,0,0],[0,1,1,0,0],[0,0,1,0,0],[0,0,0,1,1],[0,0,0,0,1]];;
-d := HomalgMatrix( d, 5, 5, GF3 );;
-d := VectorSpaceMorphism( V1, d, V1 );
-#! <A morphism in Category of matrices over GF(3)>
-Display( d );
+d := [[1,1,0,0,0],[0,1,1,0,0],[0,0,1,0,0],[0,0,0,1,1],[0,0,0,0,1]];;
+e := [[0,1,0,0],[0,0,1,0],[0,0,0,0],[0,1,0,1],[0,0,1,0]];;
+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
+#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
+#! over GF(3) defined by the following data:
+#! 
+#! 
+#! Image of <(1)>:
+#! A vector space object over GF(3) of dimension 5
+#! 
+#! Image of <(2)>:
+#! A vector space object over GF(3) of dimension 4
+#! 
+#! Image of (1)-[{ Z(3)^0*(a) }]->(1):
 #!  1 1 . . .
 #!  . 1 1 . .
 #!  . . 1 . .
 #!  . . . 1 1
 #!  . . . . 1
 #! 
 #! A morphism in Category of matrices over GF(3)
-e := One(GF3) * [[0,1,0,0],[0,0,1,0],[0,0,0,0],[0,1,0,1],[0,0,1,0]];;
-e := HomalgMatrix( e, 5, 4, GF3 );;
-e := VectorSpaceMorphism( V1, e, V2 );
-#! <A morphism in Category of matrices over GF(3)>
-Display( e );
+#! 
+#! 
+#! Image of (1)-[{ Z(3)^0*(b) }]->(2):
 #!  . 1 . .
 #!  . . 1 .
 #!  . . . .
 #!  . 1 . 1
 #!  . . 1 .
 #! 
 #! A morphism in Category of matrices over GF(3)
-f := One(GF3) * [[1,1,0,0],[0,1,1,0],[0,0,1,0],[0,0,0,1]];;
-f := HomalgMatrix( f, 4, 4, GF3 );;
-f := VectorSpaceMorphism( V2, f, V2 );
-#! <A morphism in Category of matrices over GF(3)>
-Display( f );
+#! 
+#! 
+#! Image of (2)-[{ Z(3)^0*(c) }]->(2):
 #!  1 1 . .
 #!  . 1 1 .
 #!  . . 1 .
 #!  . . . 1
 #! 
 #! A morphism in Category of matrices over GF(3)
-nine := AsObjectInHomCategory( kq, [ V1, V2 ], [ d, e, f ] );
-#! <(1)->5, (2)->4; (a)->5x5, (b)->5x4, (c)->4x4>
 nine(kq.1);
 #! <A vector space object over GF(3) of dimension 5>
 nine(kq.2);
@@ -503,7 +506,7 @@ Display( emb );
 #! Image of <(1)>:
 #!  . . 1
 #! 
-#!  A split monomorphism in Category of matrices over GF(3)
+#! A split monomorphism in Category of matrices over GF(3)
 #! 
 #! 
 #! Image of <(2)>: