diff --git a/CartesianCategories/PackageInfo.g b/CartesianCategories/PackageInfo.g index b8b886cfa4..ba5605c106 100644 --- a/CartesianCategories/PackageInfo.g +++ b/CartesianCategories/PackageInfo.g @@ -10,7 +10,7 @@ SetPackageInfo( rec( PackageName := "CartesianCategories", Subtitle := "Cartesian and cocartesian categories and various subdoctrines", -Version := "2023.08-02", +Version := "2023.08-03", Date := ~.Version{[ 1 .. 10 ]}, Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ), License := "GPL-2.0-or-later", diff --git a/CartesianCategories/gap/AUTOGENERATED_FROM.md b/CartesianCategories/gap/AUTOGENERATED_FROM.md index 759056a2d8..c33d703aae 100644 --- a/CartesianCategories/gap/AUTOGENERATED_FROM.md +++ b/CartesianCategories/gap/AUTOGENERATED_FROM.md @@ -1,3 +1,3 @@ The files of this package which include the line `THIS FILE WAS AUTOMATICALLY GENERATED` in their header have been autogenerated -* from MonoidalCategories v2023.05-02 +* from MonoidalCategories v2023.08-01 diff --git a/CartesianCategories/gap/SymmetricCartesianClosedCategoriesDerivedMethods.gi b/CartesianCategories/gap/SymmetricCartesianClosedCategoriesDerivedMethods.gi index 248388a2d0..ef795323f4 100644 --- a/CartesianCategories/gap/SymmetricCartesianClosedCategoriesDerivedMethods.gi +++ b/CartesianCategories/gap/SymmetricCartesianClosedCategoriesDerivedMethods.gi @@ -158,7 +158,7 @@ AddDerivationToCAP( MorphismToCartesianBidualWithGivenCartesianBidual, function( cat, a, avv ) local morphism, av, tensor_unit; - + # a # | # | coev_(a,a^v) @@ -230,7 +230,7 @@ AddDerivationToCAP( CartesianDualOnMorphismsWithGivenCartesianDuals, [ IsomorphismFromExponentialIntoTerminalObjectToCartesianDualObject, 1 ] ], function( cat, s, alpha, r ) - + # alpha: a → b # # b^v @@ -383,7 +383,7 @@ AddDerivationToCAP( DirectProductExponentialCompatibilityMorphismWithGivenObject # # # Adjoint[ (Exp(a1,b1) × Exp(a2,b2)) × (a1 × a2) → b1 × b2 ] = [ Exp(a1,b1) × Exp(a2,b2) → Exp(a1 × a2, b1 × b2) ] - + a1 := list[1]; b1 := list[2]; a2 := list[3]; @@ -453,7 +453,7 @@ AddDerivationToCAP( DirectProductCartesianDualityCompatibilityMorphismWithGivenO function( cat, s, a, b, r ) local morphism, unit, direct_product_on_a_and_b; - + # a^v × b^v # | # v @@ -535,7 +535,7 @@ AddDerivationToCAP( IsomorphismFromObjectToExponentialWithGivenExponential, function( cat, a, internal_hom ) local unit; - + # ρ_a: a × 1 → a # # Adjoint( ρ_a ) = ( a → Exp(1,a) ) @@ -572,7 +572,7 @@ AddDerivationToCAP( IsomorphismFromExponentialToObjectWithGivenExponential, function( cat, a, internal_hom ) local unit; - + # Exp(1,a) # | # | ( ρ_Exp(1,a) )^-1 @@ -618,7 +618,7 @@ AddDerivationToCAP( MorphismFromDirectProductToExponentialWithGivenObjects, function( cat, direct_product_object, a, b, internal_hom ) local unit; - + # a^v × b # | # v @@ -631,7 +631,7 @@ AddDerivationToCAP( MorphismFromDirectProductToExponentialWithGivenObjects, # | Exp((ρ_a)^-1, λ_b) # v # Exp(a,b) - + unit := TerminalObject( cat ); return PreComposeList( cat, [ @@ -699,7 +699,7 @@ AddDerivationToCAP( CartesianPreComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local exp_a_b, exp_b_c, morphism; - + # (Exp(a,b) × Exp(b,c)) × a # | # | α_( ( Exp(a,b), Exp(b,c) ), a) @@ -772,7 +772,7 @@ AddDerivationToCAP( CartesianPostComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local exp_a_b, exp_b_c, morphism; - + # (Exp(b,c) × Exp(a,b)) × a # | # | α_( ( Exp(b,c), Exp(a,b) ), c ) @@ -879,7 +879,7 @@ AddDerivationToCAP( DirectProductExponentialCompatibilityMorphismWithGivenObject function( cat, source, list, range ) local a1, b1, a2, b2, morphism, exp_a1_b1, exp_a2_b2, id_a2, direct_product_on_objects_exp_a1_b1_exp_a2_b2; - + # Exp(a1,b1) × Exp(a2,b2) × a1 × a2 # | # | id_Exp(a1,b1) × B_( Exp(a2,b2), a1 ) × id_a2 @@ -949,7 +949,7 @@ AddDerivationToCAP( DirectProductCartesianDualityCompatibilityMorphismWithGivenO function( cat, source, a, b, range ) local morphism, unit, direct_product_on_a_and_b; - + # a^v × b^v # | # v @@ -1054,7 +1054,7 @@ AddDerivationToCAP( CartesianPostComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local exp_a_b, exp_b_c, morphism; - + # Exp(b,c) × Exp(a,b) × a # | # | id_Exp(b,c) × ev_ab diff --git a/CartesianCategories/gap/SymmetricCocartesianCoclosedCategoriesDerivedMethods.gi b/CartesianCategories/gap/SymmetricCocartesianCoclosedCategoriesDerivedMethods.gi index 15f32a5ead..f4a81102ad 100644 --- a/CartesianCategories/gap/SymmetricCocartesianCoclosedCategoriesDerivedMethods.gi +++ b/CartesianCategories/gap/SymmetricCocartesianCoclosedCategoriesDerivedMethods.gi @@ -75,7 +75,7 @@ AddDerivationToCAP( CoexponentialToCoproductAdjunctionMap, [ IdentityMorphism, 1 ] ], function( cat, a, b, f ) - + # f: Coexp(a,b) → c # # a @@ -102,7 +102,7 @@ AddDerivationToCAP( UniversalPropertyOfCocartesianDual, [ CoproductToCoexponentialAdjunctionMap, 1 ] ], function( cat, t, a, alpha ) - + # alpha: 1 → t ⊔ a # # a_v → ( Coexp(1,a) → t ) = Adjoint( alpha ) @@ -124,7 +124,7 @@ AddDerivationToCAP( MorphismFromCocartesianBidualWithGivenCocartesianBidual, function( cat, a, avv ) local alpha; - + # 1 # | # | cocaev_a @@ -160,7 +160,7 @@ AddDerivationToCAP( MorphismFromCocartesianBidualWithGivenCocartesianBidual, function( cat, a, avv ) local morphism, av, tensor_unit; - + # Coexp(1, a_v) # | # | Coexp( cocaev_(1,a), id_(a_v) ) @@ -192,7 +192,7 @@ AddDerivationToCAP( MorphismFromCocartesianBidualWithGivenCocartesianBidual, ] ); return morphism; - + end : CategoryFilter := IsCocartesianCoclosedCategory ); ## @@ -201,7 +201,7 @@ AddDerivationToCAP( CocartesianDualOnObjects, [ [ IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject, 1 ] ], function( cat, a ) - + # Source( a_v → Coexp(1,a) ) return Source( IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject( cat, a ) ); @@ -214,7 +214,7 @@ AddDerivationToCAP( CocartesianDualOnObjects, [ [ IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject, 1 ] ], function( cat, a ) - + # Range( Coexp(1,a) → a_v ) return Range( IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject( cat, a ) ); @@ -233,7 +233,7 @@ AddDerivationToCAP( CocartesianDualOnMorphismsWithGivenCocartesianDuals, function( cat, s, alpha, r ) local result_morphism; - + # alpha: a → b # # b_v @@ -269,9 +269,9 @@ AddDerivationToCAP( CocartesianEvaluationForCocartesianDualWithGivenCoproduct, [ IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject, 1 ] ], function( cat, s, a, r ) - + # s := 1 - + # Adjoint( Coexp(1,a) → a_v ) = ( 1 → a_v ⊔ a ) return CoexponentialToCoproductAdjunctionMap( cat, @@ -291,7 +291,7 @@ AddDerivationToCAP( CocartesianLambdaIntroduction, function( cat, alpha ) local result_morphism, range; - + # a # | # | alpha @@ -324,7 +324,7 @@ AddDerivationToCAP( CocartesianLambdaElimination, function( cat, a, b, alpha ) local result_morphism; - + # alpha: Coexp(a,b) → 1 # Adjoint( alpha ) = ( a → 1 ⊔ b ) # @@ -360,7 +360,7 @@ AddDerivationToCAP( CoexponentialCoproductCompatibilityMorphismWithGivenObjects, function( cat, source, list, range ) local a1, a2, b1, b2, morphism, coexp_a1_b1, coexp_a2_b2, id_b2, coproduct_on_objects_coexp_a1_b1_coexp_a2_b2; - + # a1 ⊔ a2 # | # | id_a1 ⊔ cocaev_(a2,b2) @@ -402,7 +402,7 @@ AddDerivationToCAP( CoexponentialCoproductCompatibilityMorphismWithGivenObjects, coexp_a1_b1 := CoexponentialOnObjects( cat, a1, b1 ); coexp_a2_b2 := CoexponentialOnObjects( cat, a2, b2 ); - + id_b2 := IdentityMorphism( cat, b2 ); coproduct_on_objects_coexp_a1_b1_coexp_a2_b2 := @@ -463,7 +463,7 @@ AddDerivationToCAP( CocartesianDualityCoproductCompatibilityMorphismWithGivenObj function( cat, s, a, b, r ) local morphism, unit, coproduct_on_a_and_b; - + # (a ⊔ b)_v # | # V @@ -499,7 +499,7 @@ AddDerivationToCAP( CocartesianDualityCoproductCompatibilityMorphismWithGivenObj ] ); return morphism; - + end : CategoryFilter := IsCocartesianCoclosedCategory ); ## @@ -514,7 +514,7 @@ AddDerivationToCAP( IsomorphismFromCoexponentialToObjectWithGivenCoexponential, function( cat, a, internal_cohom ) local unit; - + # Coexp(a, 1) # | # | Coexp((ρ_a)^-1, id_1) @@ -545,7 +545,7 @@ AddDerivationToCAP( IsomorphismFromCoexponentialToObjectWithGivenCoexponential, function( cat, a, internal_cohom ) local unit; - + # (ρ_a)^-1: a → a ⊔ 1 # # Adjoint( (ρ_a)^-1 ) = ( Coexp(a,1) → a ) @@ -582,7 +582,7 @@ AddDerivationToCAP( IsomorphismFromObjectToCoexponentialWithGivenCoexponential, function( cat, a, internal_cohom ) local unit; - + # a # | # | cocaev_(a,1) @@ -628,7 +628,7 @@ AddDerivationToCAP( MorphismFromCoexponentialToCoproductWithGivenObjects, function( cat, internal_cohom, a, b, coproduct_object ) local unit; - + # Coexp(a,b) # | # | Coexp((λ_a)^-1, ρ_b) @@ -667,7 +667,7 @@ AddDerivationToCAP( CocartesianEvaluationMorphismWithGivenRange, [ CoexponentialOnObjects, 1 ] ], function( cat, a, b, coproduct_object ) - + # Adjoint( id_Coexp(a,b): Coexp(a,b) → Coexp(a,b) ) = ( a → Coexp(a,b) ⊔ b ) return CoexponentialToCoproductAdjunctionMap( cat, @@ -684,7 +684,7 @@ AddDerivationToCAP( CocartesianCoevaluationMorphismWithGivenSource, [ Coproduct, 1 ] ], function( cat, a, b, internal_cohom ) - + # Adjoint( id_(a ⊔ b): a ⊔ b → a ⊔ b ) = ( Coexp(a ⊔ b, b) → a ) return CoproductToCoexponentialAdjunctionMap( cat, @@ -710,7 +710,7 @@ AddDerivationToCAP( CocartesianPreCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local coexp_a_b, coexp_b_c, morphism; - + # a # | # | cocaev_ab @@ -783,7 +783,7 @@ AddDerivationToCAP( CocartesianPostCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local coexp_a_b, coexp_b_c, morphism; - + # a # | # | cocaev_ab @@ -833,7 +833,7 @@ AddDerivationToCAP( CocartesianPostCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local braiding; - + # Coexp(a,c) # | # | PreCoCompose @@ -891,7 +891,7 @@ AddDerivationToCAP( CoexponentialCoproductCompatibilityMorphismWithGivenObjects, function( cat, source, list, range ) local a1, a2, b1, b2, morphism, coexp_a1_b1, coexp_a2_b2, id_b2, coproduct_on_objects_coexp_a1_b1_coexp_a2_b2; - + # a1 ⊔ a2 # | # | id_a1 ⊔ cocaev_(a2,b2) @@ -961,7 +961,7 @@ AddDerivationToCAP( CocartesianDualityCoproductCompatibilityMorphismWithGivenObj function( cat, source, a, b, range ) local morphism, unit, coproduct_on_a_and_b; - + # (a ⊔ b)_v # | # V @@ -1006,7 +1006,7 @@ AddDerivationToCAP( CocartesianPreCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local coexp_a_b, coexp_b_c, morphism; - + # a # | # | cocaev_ab @@ -1066,7 +1066,7 @@ AddDerivationToCAP( CocartesianPostCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local coexp_a_b, coexp_b_c, morphism; - + # a # | # | cocaev_ab diff --git a/MonoidalCategories/PackageInfo.g b/MonoidalCategories/PackageInfo.g index d6a30c178e..1866f3a010 100644 --- a/MonoidalCategories/PackageInfo.g +++ b/MonoidalCategories/PackageInfo.g @@ -10,7 +10,7 @@ SetPackageInfo( rec( PackageName := "MonoidalCategories", Subtitle := "Monoidal and monoidal (co)closed categories", -Version := "2023.07-01", +Version := "2023.08-01", Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ), License := "GPL-2.0-or-later", diff --git a/MonoidalCategories/gap/RigidSymmetricClosedMonoidalCategoriesDerivedMethods.gi b/MonoidalCategories/gap/RigidSymmetricClosedMonoidalCategoriesDerivedMethods.gi index e1a9201461..799d36e670 100644 --- a/MonoidalCategories/gap/RigidSymmetricClosedMonoidalCategoriesDerivedMethods.gi +++ b/MonoidalCategories/gap/RigidSymmetricClosedMonoidalCategoriesDerivedMethods.gi @@ -23,7 +23,7 @@ AddDerivationToCAP( InternalHomOnObjects, [ [ IsomorphismFromTensorProductWithDualObjectToInternalHom, 1 ] ], function( cat, a, b ) - + # Range( a^v ⊗ b → Hom(a,b) ) return Range( IsomorphismFromTensorProductWithDualObjectToInternalHom( cat, a, b ) ); @@ -41,7 +41,7 @@ AddDerivationToCAP( InternalHomOnMorphismsWithGivenInternalHoms, function( cat, internal_hom_source, alpha, beta, internal_hom_range ) local dual_alpha; - + # alpha: a → a' # beta: b → b' # @@ -76,7 +76,7 @@ AddDerivationToCAP( MorphismFromBidualWithGivenBidual, [ MorphismToBidualWithGivenBidual, 1 ] ], function( cat, a, bidual ) - + # Inverse( a → (a^v)^v ) return InverseForMorphisms( cat, MorphismToBidualWithGivenBidual( cat, a, bidual ) ); @@ -90,7 +90,7 @@ AddDerivationToCAP( MorphismToBidualWithGivenBidual, [ MorphismFromBidualWithGivenBidual, 1 ] ], function( cat, a, bidual ) - + # Inverse( (a^v)^v → a ) return InverseForMorphisms( cat, MorphismFromBidualWithGivenBidual( cat, a, bidual ) ); @@ -112,7 +112,7 @@ AddDerivationToCAP( EvaluationMorphismWithGivenSource, function( cat, a, b, internal_hom_tensored_a ) local morphism; - + # Hom(a,b) ⊗ a # | # | Isomorphism ⊗ id_a @@ -170,7 +170,7 @@ AddDerivationToCAP( EvaluationMorphismWithGivenSource, function( cat, a, b, internal_hom_tensored_a ) local morphism; - + # Hom(a,b) ⊗ a # | # | Isomorphism ⊗ id_a @@ -200,7 +200,7 @@ AddDerivationToCAP( EvaluationMorphismWithGivenSource, ] ); return morphism; - + end : CategoryFilter := cat -> HasIsRigidSymmetricClosedMonoidalCategory( cat ) and IsRigidSymmetricClosedMonoidalCategory( cat ) and HasIsStrictMonoidalCategory( cat ) and IsStrictMonoidalCategory( cat ) ); ## @@ -219,7 +219,7 @@ AddDerivationToCAP( CoevaluationMorphismWithGivenRange, function( cat, a, b, internal_hom ) local morphism, dual_b, id_a; - + # a # | # | (λ_a)^-1 @@ -290,7 +290,7 @@ AddDerivationToCAP( CoevaluationMorphismWithGivenRange, function( cat, a, b, internal_hom ) local morphism, dual_b, id_a; - + # 1 ⊗ a # | # | coev_b ⊗ id_a @@ -439,7 +439,7 @@ AddDerivationToCAP( CoevaluationForDualWithGivenTensorProduct, function( cat, unit, a, tensor_object ) local morphism; - + # 1 # | # | LambdaIntro( id_a ) @@ -476,7 +476,7 @@ AddDerivationToCAP( TraceMap, function( cat, alpha ) local result_morphism, a; - + # alpha: a → a # # 1 @@ -524,7 +524,7 @@ AddDerivationToCAP( TensorProductInternalHomCompatibilityMorphismInverseWithGive [ TensorProductInternalHomCompatibilityMorphismWithGivenObjects, 1 ] ], function( cat, source, list, range ) - + # Inverse( Hom(a,a') ⊗ Hom(b,b') → Hom(a ⊗ b, a' ⊗ b') ) return InverseForMorphisms( cat, TensorProductInternalHomCompatibilityMorphismWithGivenObjects( cat, range, list, source ) ); diff --git a/MonoidalCategories/gap/RigidSymmetricCoclosedMonoidalCategoriesDerivedMethods.gi b/MonoidalCategories/gap/RigidSymmetricCoclosedMonoidalCategoriesDerivedMethods.gi index d73e2bdcdb..28b0cb5fcd 100644 --- a/MonoidalCategories/gap/RigidSymmetricCoclosedMonoidalCategoriesDerivedMethods.gi +++ b/MonoidalCategories/gap/RigidSymmetricCoclosedMonoidalCategoriesDerivedMethods.gi @@ -10,7 +10,7 @@ AddDerivationToCAP( InternalCoHomOnObjects, [ [ IsomorphismFromInternalCoHomToTensorProductWithCoDualObject, 1 ] ], function( cat, a, b ) - + # Source( Cohom(a,b) → b_v ⊗ a ) return Source( IsomorphismFromInternalCoHomToTensorProductWithCoDualObject( cat, a, b ) ); @@ -23,7 +23,7 @@ AddDerivationToCAP( InternalCoHomOnObjects, [ [ IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom, 1 ] ], function( cat, a, b ) - + # Range( b_v ⊗ a → Cohom(a,b) ) return Range( IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom( cat, b, a ) ); @@ -41,7 +41,7 @@ AddDerivationToCAP( InternalCoHomOnMorphismsWithGivenInternalCoHoms, function( cat, internal_cohom_source, alpha, beta, internal_cohom_range ) local codual_beta; - + # alpha: a → a' # beta: b → b' # @@ -76,7 +76,7 @@ AddDerivationToCAP( MorphismToCoBidualWithGivenCoBidual, [ MorphismFromCoBidualWithGivenCoBidual, 1 ] ], function( cat, a, cobidual ) - + # Inverse( (a_v)_v → a ) return InverseForMorphisms( cat, MorphismFromCoBidualWithGivenCoBidual( cat, a, cobidual ) ); @@ -90,7 +90,7 @@ AddDerivationToCAP( MorphismFromCoBidualWithGivenCoBidual, [ MorphismToCoBidualWithGivenCoBidual, 1 ] ], function( cat, a, cobidual ) - + # Inverse( a → (a_v)_v ) return InverseForMorphisms( cat, MorphismToCoBidualWithGivenCoBidual( cat, a, cobidual ) ); @@ -112,7 +112,7 @@ AddDerivationToCAP( CoclosedEvaluationMorphismWithGivenRange, function( cat, a, b, internal_cohom_tensored_b ) local morphism; - + # a # | # | (ρ_a)^-1 @@ -170,7 +170,7 @@ AddDerivationToCAP( CoclosedEvaluationMorphismWithGivenRange, function( cat, a, b, internal_cohom_tensored_b ) local morphism; - + # a ⊗ 1 # | # | id_a ⊗ coclev_b @@ -200,7 +200,7 @@ AddDerivationToCAP( CoclosedEvaluationMorphismWithGivenRange, ] ); return morphism; - + end : CategoryFilter := cat -> HasIsRigidSymmetricCoclosedMonoidalCategory( cat ) and IsRigidSymmetricCoclosedMonoidalCategory( cat ) and HasIsStrictMonoidalCategory( cat ) and IsStrictMonoidalCategory( cat ) ); ## @@ -219,7 +219,7 @@ AddDerivationToCAP( CoclosedCoevaluationMorphismWithGivenSource, function( cat, a, b, internal_cohom ) local morphism, codual_b, id_a; - + # Cohom(a ⊗ b, b) # | # | Isomorphism @@ -290,7 +290,7 @@ AddDerivationToCAP( CoclosedCoevaluationMorphismWithGivenSource, function( cat, a, b, internal_cohom ) local morphism, codual_b, id_a; - + # Cohom(a ⊗ b, b) # | # | Isomorphism @@ -391,7 +391,7 @@ AddDerivationToCAP( CoclosedCoevaluationForCoDualWithGivenTensorProduct, function( cat, tensor_object, a, unit ) local morphism; - + # a ⊗ a_v # | # | B_( a, a_v ) @@ -428,7 +428,7 @@ AddDerivationToCAP( CoTraceMap, function( cat, alpha ) local a; - + # alpha: a → a # # 1 @@ -474,7 +474,7 @@ AddDerivationToCAP( InternalCoHomTensorProductCompatibilityMorphismInverseWithGi [ InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects, 1 ] ], function( cat, source, list, range ) - + # Inverse( Cohom( a ⊗ a', b ⊗ b') → Cohom(a,b) ⊗ Cohom(a',b') ) return InverseForMorphisms( cat, InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects( cat, range, list, source ) ); diff --git a/MonoidalCategories/gap/SymmetricClosedMonoidalCategoriesDerivedMethods.gi b/MonoidalCategories/gap/SymmetricClosedMonoidalCategoriesDerivedMethods.gi index c435994f9d..e3e4920dd8 100644 --- a/MonoidalCategories/gap/SymmetricClosedMonoidalCategoriesDerivedMethods.gi +++ b/MonoidalCategories/gap/SymmetricClosedMonoidalCategoriesDerivedMethods.gi @@ -155,7 +155,7 @@ AddDerivationToCAP( MorphismToBidualWithGivenBidual, function( cat, a, avv ) local morphism, av, tensor_unit; - + # a # | # | coev_(a,a^v) @@ -227,7 +227,7 @@ AddDerivationToCAP( DualOnMorphismsWithGivenDuals, [ IsomorphismFromInternalHomIntoTensorUnitToDualObject, 1 ] ], function( cat, s, alpha, r ) - + # alpha: a → b # # b^v @@ -380,7 +380,7 @@ AddDerivationToCAP( TensorProductInternalHomCompatibilityMorphismWithGivenObject # # # Adjoint[ (Hom(a1,b1) ⊗ Hom(a2,b2)) ⊗ (a1 ⊗ a2) → b1 ⊗ b2 ] = [ Hom(a1,b1) ⊗ Hom(a2,b2) → Hom(a1 ⊗ a2, b1 ⊗ b2) ] - + a1 := list[1]; b1 := list[2]; a2 := list[3]; @@ -450,7 +450,7 @@ AddDerivationToCAP( TensorProductDualityCompatibilityMorphismWithGivenObjects, function( cat, s, a, b, r ) local morphism, unit, tensor_product_on_a_and_b; - + # a^v ⊗ b^v # | # v @@ -532,7 +532,7 @@ AddDerivationToCAP( IsomorphismFromObjectToInternalHomWithGivenInternalHom, function( cat, a, internal_hom ) local unit; - + # ρ_a: a ⊗ 1 → a # # Adjoint( ρ_a ) = ( a → Hom(1,a) ) @@ -569,7 +569,7 @@ AddDerivationToCAP( IsomorphismFromInternalHomToObjectWithGivenInternalHom, function( cat, a, internal_hom ) local unit; - + # Hom(1,a) # | # | ( ρ_Hom(1,a) )^-1 @@ -615,7 +615,7 @@ AddDerivationToCAP( MorphismFromTensorProductToInternalHomWithGivenObjects, function( cat, tensor_object, a, b, internal_hom ) local unit; - + # a^v ⊗ b # | # v @@ -628,7 +628,7 @@ AddDerivationToCAP( MorphismFromTensorProductToInternalHomWithGivenObjects, # | Hom((ρ_a)^-1, λ_b) # v # Hom(a,b) - + unit := TensorUnit( cat ); return PreComposeList( cat, [ @@ -696,7 +696,7 @@ AddDerivationToCAP( MonoidalPreComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local hom_a_b, hom_b_c, morphism; - + # (Hom(a,b) ⊗ Hom(b,c)) ⊗ a # | # | α_( ( Hom(a,b), Hom(b,c) ), a) @@ -769,7 +769,7 @@ AddDerivationToCAP( MonoidalPostComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local hom_a_b, hom_b_c, morphism; - + # (Hom(b,c) ⊗ Hom(a,b)) ⊗ a # | # | α_( ( Hom(b,c), Hom(a,b) ), c ) @@ -876,7 +876,7 @@ AddDerivationToCAP( TensorProductInternalHomCompatibilityMorphismWithGivenObject function( cat, source, list, range ) local a1, b1, a2, b2, morphism, int_hom_a1_b1, int_hom_a2_b2, id_a2, tensor_product_on_objects_int_hom_a1_b1_int_hom_a2_b2; - + # Hom(a1,b1) ⊗ Hom(a2,b2) ⊗ a1 ⊗ a2 # | # | id_Hom(a1,b1) ⊗ B_( Hom(a2,b2), a1 ) ⊗ id_a2 @@ -946,7 +946,7 @@ AddDerivationToCAP( TensorProductDualityCompatibilityMorphismWithGivenObjects, function( cat, source, a, b, range ) local morphism, unit, tensor_product_on_a_and_b; - + # a^v ⊗ b^v # | # v @@ -1051,7 +1051,7 @@ AddDerivationToCAP( MonoidalPostComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local hom_a_b, hom_b_c, morphism; - + # Hom(b,c) ⊗ Hom(a,b) ⊗ a # | # | id_Hom(b,c) ⊗ ev_ab diff --git a/MonoidalCategories/gap/SymmetricCoclosedMonoidalCategoriesDerivedMethods.gi b/MonoidalCategories/gap/SymmetricCoclosedMonoidalCategoriesDerivedMethods.gi index e50d82c4ac..7759daae18 100644 --- a/MonoidalCategories/gap/SymmetricCoclosedMonoidalCategoriesDerivedMethods.gi +++ b/MonoidalCategories/gap/SymmetricCoclosedMonoidalCategoriesDerivedMethods.gi @@ -72,7 +72,7 @@ AddDerivationToCAP( InternalCoHomToTensorProductAdjunctionMap, [ IdentityMorphism, 1 ] ], function( cat, a, b, f ) - + # f: Cohom(a,b) → c # # a @@ -99,7 +99,7 @@ AddDerivationToCAP( UniversalPropertyOfCoDual, [ TensorProductToInternalCoHomAdjunctionMap, 1 ] ], function( cat, t, a, alpha ) - + # alpha: 1 → t ⊗ a # # a_v → ( Cohom(1,a) → t ) = Adjoint( alpha ) @@ -121,7 +121,7 @@ AddDerivationToCAP( MorphismFromCoBidualWithGivenCoBidual, function( cat, a, avv ) local alpha; - + # 1 # | # | coclev_a @@ -157,7 +157,7 @@ AddDerivationToCAP( MorphismFromCoBidualWithGivenCoBidual, function( cat, a, avv ) local morphism, av, tensor_unit; - + # Cohom(1, a_v) # | # | Cohom( coclev_(1,a), id_(a_v) ) @@ -189,7 +189,7 @@ AddDerivationToCAP( MorphismFromCoBidualWithGivenCoBidual, ] ); return morphism; - + end : CategoryFilter := IsSymmetricCoclosedMonoidalCategory ); ## @@ -198,7 +198,7 @@ AddDerivationToCAP( CoDualOnObjects, [ [ IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit, 1 ] ], function( cat, a ) - + # Source( a_v → Cohom(1,a) ) return Source( IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit( cat, a ) ); @@ -211,7 +211,7 @@ AddDerivationToCAP( CoDualOnObjects, [ [ IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject, 1 ] ], function( cat, a ) - + # Range( Cohom(1,a) → a_v ) return Range( IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject( cat, a ) ); @@ -230,7 +230,7 @@ AddDerivationToCAP( CoDualOnMorphismsWithGivenCoDuals, function( cat, s, alpha, r ) local result_morphism; - + # alpha: a → b # # b_v @@ -266,9 +266,9 @@ AddDerivationToCAP( CoclosedEvaluationForCoDualWithGivenTensorProduct, [ IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject, 1 ] ], function( cat, s, a, r ) - + # s := 1 - + # Adjoint( Cohom(1,a) → a_v ) = ( 1 → a_v ⊗ a ) return InternalCoHomToTensorProductAdjunctionMap( cat, @@ -288,7 +288,7 @@ AddDerivationToCAP( CoLambdaIntroduction, function( cat, alpha ) local result_morphism, range; - + # a # | # | alpha @@ -321,7 +321,7 @@ AddDerivationToCAP( CoLambdaElimination, function( cat, a, b, alpha ) local result_morphism; - + # alpha: Cohom(a,b) → 1 # Adjoint( alpha ) = ( a → 1 ⊗ b ) # @@ -357,7 +357,7 @@ AddDerivationToCAP( InternalCoHomTensorProductCompatibilityMorphismWithGivenObje function( cat, source, list, range ) local a1, a2, b1, b2, morphism, int_cohom_a1_b1, int_cohom_a2_b2, id_b2, tensor_product_on_objects_int_cohom_a1_b1_int_cohom_a2_b2; - + # a1 ⊗ a2 # | # | id_a1 ⊗ coclev_(a2,b2) @@ -399,7 +399,7 @@ AddDerivationToCAP( InternalCoHomTensorProductCompatibilityMorphismWithGivenObje int_cohom_a1_b1 := InternalCoHomOnObjects( cat, a1, b1 ); int_cohom_a2_b2 := InternalCoHomOnObjects( cat, a2, b2 ); - + id_b2 := IdentityMorphism( cat, b2 ); tensor_product_on_objects_int_cohom_a1_b1_int_cohom_a2_b2 := @@ -460,7 +460,7 @@ AddDerivationToCAP( CoDualityTensorProductCompatibilityMorphismWithGivenObjects, function( cat, s, a, b, r ) local morphism, unit, tensor_product_on_a_and_b; - + # (a ⊗ b)_v # | # V @@ -496,7 +496,7 @@ AddDerivationToCAP( CoDualityTensorProductCompatibilityMorphismWithGivenObjects, ] ); return morphism; - + end : CategoryFilter := IsSymmetricCoclosedMonoidalCategory ); ## @@ -511,7 +511,7 @@ AddDerivationToCAP( IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom, function( cat, a, internal_cohom ) local unit; - + # Cohom(a, 1) # | # | Cohom((ρ_a)^-1, id_1) @@ -542,7 +542,7 @@ AddDerivationToCAP( IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom, function( cat, a, internal_cohom ) local unit; - + # (ρ_a)^-1: a → a ⊗ 1 # # Adjoint( (ρ_a)^-1 ) = ( Cohom(a,1) → a ) @@ -579,7 +579,7 @@ AddDerivationToCAP( IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom, function( cat, a, internal_cohom ) local unit; - + # a # | # | coclev_(a,1) @@ -625,7 +625,7 @@ AddDerivationToCAP( MorphismFromInternalCoHomToTensorProductWithGivenObjects, function( cat, internal_cohom, a, b, tensor_object ) local unit; - + # Cohom(a,b) # | # | Cohom((λ_a)^-1, ρ_b) @@ -664,7 +664,7 @@ AddDerivationToCAP( CoclosedEvaluationMorphismWithGivenRange, [ InternalCoHomOnObjects, 1 ] ], function( cat, a, b, tensor_object ) - + # Adjoint( id_Cohom(a,b): Cohom(a,b) → Cohom(a,b) ) = ( a → Cohom(a,b) ⊗ b ) return InternalCoHomToTensorProductAdjunctionMap( cat, @@ -681,7 +681,7 @@ AddDerivationToCAP( CoclosedCoevaluationMorphismWithGivenSource, [ TensorProductOnObjects, 1 ] ], function( cat, a, b, internal_cohom ) - + # Adjoint( id_(a ⊗ b): a ⊗ b → a ⊗ b ) = ( Cohom(a ⊗ b, b) → a ) return TensorProductToInternalCoHomAdjunctionMap( cat, @@ -707,7 +707,7 @@ AddDerivationToCAP( MonoidalPreCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local cohom_a_b, cohom_b_c, morphism; - + # a # | # | coclev_ab @@ -780,7 +780,7 @@ AddDerivationToCAP( MonoidalPostCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local cohom_a_b, cohom_b_c, morphism; - + # a # | # | coclev_ab @@ -830,7 +830,7 @@ AddDerivationToCAP( MonoidalPostCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local braiding; - + # Cohom(a,c) # | # | PreCoCompose @@ -888,7 +888,7 @@ AddDerivationToCAP( InternalCoHomTensorProductCompatibilityMorphismWithGivenObje function( cat, source, list, range ) local a1, a2, b1, b2, morphism, int_cohom_a1_b1, int_cohom_a2_b2, id_b2, tensor_product_on_objects_int_cohom_a1_b1_int_cohom_a2_b2; - + # a1 ⊗ a2 # | # | id_a1 ⊗ coclev_(a2,b2) @@ -958,7 +958,7 @@ AddDerivationToCAP( CoDualityTensorProductCompatibilityMorphismWithGivenObjects, function( cat, source, a, b, range ) local morphism, unit, tensor_product_on_a_and_b; - + # (a ⊗ b)_v # | # V @@ -1003,7 +1003,7 @@ AddDerivationToCAP( MonoidalPreCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local cohom_a_b, cohom_b_c, morphism; - + # a # | # | coclev_ab @@ -1063,7 +1063,7 @@ AddDerivationToCAP( MonoidalPostCoComposeMorphismWithGivenObjects, function( cat, source, a, b, c, range ) local cohom_a_b, cohom_b_c, morphism; - + # a # | # | coclev_ab