diff --git a/PackageInfo.g b/PackageInfo.g index 74155cc..217636b 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -11,7 +11,7 @@ SetPackageInfo( rec( PackageName := "CatReps", Subtitle := "Representations and cohomology of finite categories", Version := Maximum( [ - "2020.02.23", ## Mohamed's version + "2020.04.02", ## Mohamed's version ## this line prevents merge conflicts "2020.01.01", ## Tibor's version ## this line prevents merge conflicts @@ -110,7 +110,7 @@ Dependencies := rec( [ "SubcategoriesForCAP", ">= 2020.02.02" ], [ "MatricesForHomalg", ">= 2020.02.02" ], [ "Toposes", ">= 2020.02.19" ], - [ "FunctorCategories", ">= 2020.02.23" ], + [ "FunctorCategories", ">= 2020.04.02" ], ], SuggestedOtherPackages := [ ], ExternalConditions := [ ], diff --git a/examples/ConcreteCategoryWithEndomorphismGroups.g b/examples/ConcreteCategoryWithEndomorphismGroups.g index fa6b0c6..d0973ea 100644 --- a/examples/ConcreteCategoryWithEndomorphismGroups.g +++ b/examples/ConcreteCategoryWithEndomorphismGroups.g @@ -80,25 +80,24 @@ CatReps := CategoryOfRepresentations( kq, kmat ); #! 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) InfoOfInstalledOperationsOfCategory( CatReps ); -#! 102 primitive operations were used to derive 207 operations for this category which +#! 109 primitive operations were used to derive 230 operations for this category which #! * IsLinearCategoryOverCommutativeRing #! * IsSymmetricMonoidalCategory #! * IsAbelianCategory CommutativeRingOfLinearCategory( CatReps ); #! GF(3) zero := ZeroObject( CatReps ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->0, (2)->0; (a)->0x0, (b)->0x0, (c)->0x0> Display( zero ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 0 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 0 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -118,18 +117,17 @@ Display( zero ); #! #! A zero, identity morphism in Category of matrices over GF(3) unit := TensorUnit( CatReps ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->1, (2)->1; (a)->1x1, (b)->1x1, (c)->1x1> Display( unit ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 1 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 1 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -188,8 +186,7 @@ Display( f ); #! #! A morphism in Category of matrices over GF(3) nine := AsObjectInHomCategory( kq, [ V1, V2 ], [ d, e, f ] ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->5, (2)->4; (a)->5x5, (b)->5x4, (c)->4x4> nine(kq.1); #! nine(kq.2); @@ -207,8 +204,7 @@ Display( nine(kq.b) ); IsWellDefined( nine ); #! true fortyone := TensorProductOnObjects( nine, nine ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->25, (2)->16; (a)->25x25, (b)->25x16, (c)->16x16> IsWellDefined( fortyone ); #! true fortyone( kq.1 ); @@ -227,10 +223,10 @@ Display( fortyone ); #! over GF(3) defined by the following data: #! #! -#! Image of (1): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 25 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 16 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -318,21 +314,19 @@ d := List( etas, eta -> List( SetOfObjects( kq ), #! [ [ 3, 0 ], [ 3, 1 ], [ 3, 3 ], [ 3, 3 ], [ 0, 3 ], #! [ 3, 0 ], [ 3, 0 ], [ 3, 0 ], [ 1, 3 ], [ 3, 3 ] ] eta := etas[3]; -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->3x25, (2)->3x16> six := Source( eta ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->3, (2)->3; (a)->3x3, (b)->3x3, (c)->3x3> Display( six ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 3 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 3 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -358,21 +352,19 @@ Display( six ); #! #! A morphism in Category of matrices over GF(3) eta2 := TensorProductOnMorphisms( eta, eta ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->9x625, (2)->9x256> thirtyfive := CokernelObject( eta ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->22, (2)->13; (a)->22x22, (b)->22x13, (c)->13x13> Display( thirtyfive ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 22 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 13 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -446,23 +438,21 @@ Display( thirtyfive ); #! #! A morphism in Category of matrices over GF(3) iso := UniversalMorphismFromDirectSum( etas ); -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->25x25, (2)->16x16> IsIsomorphism( iso ); #! true iso; -#! 1,b:1->2,c:2->2] -> Category of matrices over GF(3)> +#! <(1)->25x25, (2)->16x16> Display( Source( iso ) ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 25 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 16 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -550,7 +540,7 @@ Display( iso ); #! over GF(3) defined by the following data: #! #! -#! Image of (1): +#! Image of <(1)>: #! . . 1 . . . 2 1 . 1 1 . . 2 . . . 1 . . . . . . . #! . . . . . . . . . . . . . . . . . . . . . . 1 . . #! . 1 2 . 2 1 1 2 2 2 1 . . 2 . . 1 . . 2 2 . . 1 . @@ -580,7 +570,7 @@ Display( iso ); #! An isomorphism in Category of matrices over GF(3) #! #! -#! Image of (2): +#! Image of <(2)>: #! . . . . . . . . . . . . . . . 1 #! . . . . . . . . . . . . 1 . . . #! . . . . . . . . . . . . . 1 . . @@ -600,19 +590,17 @@ Display( iso ); #! #! An isomorphism in Category of matrices over GF(3) proj1 := YonedaProjective( CatReps, kq.1 ); -#! 1,b:1->2,c:2->2] -#! -> Category of matrices over GF(3)> +#! <(1)->3, (2)->3; (a)->3x3, (b)->3x3, (c)->3x3> Display( proj1 ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 3 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 3 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): @@ -638,28 +626,30 @@ Display( proj1 ); #! #! A morphism in Category of matrices over GF(3) proj2 := YonedaProjective( CatReps, kq.2 ); -#! 1,b:1->2,c:2->2] -#! -> Category of matrices over GF(3)> +#! <(1)->0, (2)->3; (a)->0x0, (b)->0x3, (c)->3x3> Display( proj2 ); #! 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): +#! Image of <(1)>: #! A vector space object over GF(3) of dimension 0 #! -#! Image of (2): +#! Image of <(2)>: #! A vector space object over GF(3) of dimension 3 #! #! Image of (1)-[{ Z(3)^0*(a) }]->(1): #! (an empty 0 x 0 matrix) +#! +#! A zero, isomorphism in Category of matrices over GF(3) #! #! #! Image of (1)-[{ Z(3)^0*(b) }]->(2): #! (an empty 0 x 3 matrix) #! +#! A zero, split monomorphism in Category of matrices over GF(3) +#! #! #! Image of (2)-[{ Z(3)^0*(c) }]->(2): #! . 1 .