diff --git a/PackageInfo.g b/PackageInfo.g index c0ccc8c..9ec29d4 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -11,7 +11,7 @@ SetPackageInfo( rec( PackageName := "CatReps", Subtitle := "Representations and cohomology of finite categories", Version := Maximum( [ - "2020.04.06", ## 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 := [ ], diff --git a/examples/CategoryOfRepresentations.g b/examples/CategoryOfRepresentations.g index 8507265..bfce9ed 100644 --- a/examples/CategoryOfRepresentations.g +++ b/examples/CategoryOfRepresentations.g @@ -133,15 +133,24 @@ Display( const ); #! 1 #! #! An identity morphism in Category of matrices over GF(3) -V1 := VectorSpaceObject( 5, GF3 ); -#! -V2 := VectorSpaceObject( 4, GF3 ); -#! -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 ); -#! -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 . . @@ -149,11 +158,9 @@ Display( d ); #! . . . . 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 ); -#! -Display( e ); +#! +#! +#! Image of (1)-[{ Z(3)^0*(b) }]->(2): #! . 1 . . #! . . 1 . #! . . . . @@ -161,19 +168,15 @@ Display( e ); #! . . 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 ); -#! -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); #! 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)>: