Merge pull request #704 from zickgraf/MonoidalCategories

Call CAP operations in MonoidalCategories with category as first argument

Author: zickgraf

CAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "CAP",
 Subtitle := "Categories, Algorithms, Programming",
-Version := "2021.08-03",
+Version := "2021.08-04",
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),
 License := "GPL-2.0-or-later",
 

CAP/gap/CategoryMorphisms.gd

@@ -1292,7 +1292,7 @@ DeclareOperation( "PreCompose",
 #! This is a convenience method.
 #! The argument is a list of morphisms
 #! $L = ( \alpha_1: a_1 \rightarrow a_2, \alpha_2: a_2 \rightarrow a_3, \dots, \alpha_n: a_n \rightarrow a_{n+1} )$.
-#! The output is the composition 
+#! The output is the composition
 #! $\alpha_{n} \circ ( \alpha_{n-1} \circ ( \dots ( \alpha_2 \circ \alpha_1 ) ) )$.
 #! @Returns a morphism in $\mathrm{Hom}(a_1, a_{n+1})$
 #! @Arguments L
@@ -1318,6 +1318,17 @@ DeclareOperation( "AddPreCompose",
 DeclareOperation( "AddPreCompose",
                   [ IsCapCategory, IsList ] );
 
+#! @Description
+#! This is a convenience method.
+#! The arguments are a category $C$ and a list of morphisms
+#! $L = ( \alpha_1: a_1 \rightarrow a_2, \alpha_2: a_2 \rightarrow a_3, \dots, \alpha_n: a_n \rightarrow a_{n+1} )$ in $C$.
+#! The output is the composition
+#! $\alpha_{n} \circ ( \alpha_{n-1} \circ ( \dots ( \alpha_2 \circ \alpha_1 ) ) )$.
+#! @Returns a morphism in $\mathrm{Hom}(a_1, a_{n+1})$
+#! @Arguments C, L
+DeclareOperation( "PreComposeList",
+                  [ IsCapCategory, IsList ] );
+
 
 #! @Description
 #! The arguments are two morphisms $\beta: b \rightarrow c$, $\alpha: a \rightarrow b$.
@@ -1331,7 +1342,7 @@ DeclareOperation( "PostCompose",
 #! This is a convenience method.
 #! The argument is a list of morphisms
 #! $L = ( \alpha_n: a_n \rightarrow a_{n+1}, \alpha_{n-1}: a_{n-1} \rightarrow a_n, \dots, \alpha_1: a_1 \rightarrow a_2 )$.
-#! The output is the composition 
+#! The output is the composition
 #! $((\alpha_{n} \circ  \alpha_{n-1}) \circ \dots  \alpha_2) \circ \alpha_1$.
 #! @Returns a morphism in $\mathrm{Hom}(a_1, a_{n+1})$
 #! @Arguments L
@@ -1357,6 +1368,17 @@ DeclareOperation( "AddPostCompose",
 DeclareOperation( "AddPostCompose",
                   [ IsCapCategory, IsList ] );
 
+#! @Description
+#! This is a convenience method.
+#! The arguments are a category $C$ and a list of morphisms
+#! $L = ( \alpha_n: a_n \rightarrow a_{n+1}, \alpha_{n-1}: a_{n-1} \rightarrow a_n, \dots, \alpha_1: a_1 \rightarrow a_2 )$.
+#! The output is the composition
+#! $((\alpha_{n} \circ  \alpha_{n-1}) \circ \dots  \alpha_2) \circ \alpha_1$.
+#! @Returns a morphism in $\mathrm{Hom}(a_1, a_{n+1})$
+#! @Arguments C, L
+DeclareOperation( "PostComposeList",
+                  [ IsCapCategory, IsList ] );
+
 
 ###################################
 ##

CAP/gap/CategoryMorphisms.gi

@@ -475,25 +475,24 @@ InstallMethod( PreCompose,
                [ IsList ],
 
   function( morphism_list )
-    local length, result_morphism, i;
 
-    length := Length( morphism_list );
-    
-    if length = 0 then
-      
-      Error( "non-empty list expected" );
-      
+    if IsEmpty( morphism_list ) then
+        
+        Error( "non-empty list expected" );
+        
     fi;
 
-    result_morphism := morphism_list[1];
+    return PreComposeList( CapCategory( morphism_list[1] ), morphism_list );
 
-    for i in [ 2 .. length ] do
-      
-      result_morphism := PreCompose( result_morphism, morphism_list[i] );
-      
-    od;
+end );
+
+##
+InstallMethodForCompilerForCAP( PreComposeList,
+                                [ IsCapCategory, IsList ],
+                                
+  function( cat, morphism_list )
 
-    return result_morphism;
+    return Iterated( morphism_list, { alpha, beta } -> PreCompose( cat, alpha, beta ) );
 
 end );
 
@@ -502,25 +501,24 @@ InstallMethod( PostCompose,
                [ IsList ],
 
   function( morphism_list )
-    local length, result_morphism, i;
 
-    length := Length( morphism_list );
-    
-    if length = 0 then
-      
-      Error( "non-empty list expected" );
-      
+    if IsEmpty( morphism_list ) then
+        
+        Error( "non-empty list expected" );
+        
     fi;
 
-    result_morphism := morphism_list[1];
+    return PostComposeList( CapCategory( morphism_list[1] ), morphism_list );
 
-    for i in [ 2 .. length ] do
-      
-      result_morphism := PostCompose( result_morphism, morphism_list[i] );
-      
-    od;
+end );
+
+##
+InstallMethodForCompilerForCAP( PostComposeList,
+                                [ IsCapCategory, IsList ],
+                                
+  function( cat, morphism_list )
 
-    return result_morphism;
+    return Iterated( morphism_list, { beta, alpha } -> PostCompose( cat, beta, alpha ) );
 
 end );
 

MonoidalCategories/PackageInfo.g

@@ -10,8 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "MonoidalCategories",
 Subtitle := "Monoidal and monoidal (co)closed categories",
-Version := "2021.08-01",
-
+Version := "2021.08-02",
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),
 License := "GPL-2.0-or-later",
 
@@ -120,7 +119,7 @@ Dependencies := rec(
   NeededOtherPackages := [
                    [ "GAPDoc", ">= 1.5" ],
                    [ "ToolsForHomalg", ">= 2018.05.22" ],
-                   [ "CAP", ">= 2021.08-03" ],
+                   [ "CAP", ">= 2021.08-04" ],
                    ],
   SuggestedOtherPackages := [ ],
   ExternalConditions := [ ],

MonoidalCategories/gap/AdditiveMonoidalCategories.gi

@@ -4,9 +4,9 @@ AddDerivationToCAP( LeftDistributivityExpanding,
   function( cat, object, summands_list )
     local source_and_range;
 
-    source_and_range := TensorProductOnObjects( object, DirectSum( summands_list ) );
+    source_and_range := TensorProductOnObjects( cat, object, DirectSum( cat, summands_list ) );
 
-    return LeftDistributivityExpandingWithGivenObjects(
+    return LeftDistributivityExpandingWithGivenObjects( cat,
              source_and_range,
              object, summands_list,
              source_and_range
@@ -21,9 +21,9 @@ AddDerivationToCAP( LeftDistributivityFactoring,
   function( cat, object, summands_list )
     local source_and_range;
 
-    source_and_range := TensorProductOnObjects( object, DirectSum( summands_list ) );
+    source_and_range := TensorProductOnObjects( cat, object, DirectSum( cat, summands_list ) );
 
-    return LeftDistributivityFactoringWithGivenObjects(
+    return LeftDistributivityFactoringWithGivenObjects( cat,
              source_and_range,
              object, summands_list,
              source_and_range
@@ -38,9 +38,9 @@ AddDerivationToCAP( RightDistributivityExpanding,
   function( cat, summands_list, object )
     local source_and_range;
 
-    source_and_range := TensorProductOnObjects( DirectSum( summands_list ), object );
+    source_and_range := TensorProductOnObjects( cat, DirectSum( cat, summands_list ), object );
 
-    return RightDistributivityExpandingWithGivenObjects(
+    return RightDistributivityExpandingWithGivenObjects( cat,
              source_and_range,
              summands_list, object,
              source_and_range
@@ -55,9 +55,9 @@ AddDerivationToCAP( RightDistributivityFactoring,
   function( cat, summands_list, object )
     local source_and_range;
 
-    source_and_range := TensorProductOnObjects( DirectSum( summands_list ), object );
+    source_and_range := TensorProductOnObjects( cat, DirectSum( cat, summands_list ), object );
 
-    return RightDistributivityFactoringWithGivenObjects(
+    return RightDistributivityFactoringWithGivenObjects( cat,
              source_and_range,
              summands_list, object,
              source_and_range

MonoidalCategories/gap/AdditiveMonoidalCategoriesDerivedMethods.gi

@@ -6,15 +6,15 @@ AddDerivationToCAP( LeftDistributivityExpandingWithGivenObjects,
 
     nr_summands := Size( summands );
 
-    id := IdentityMorphism( object );
+    id := IdentityMorphism( cat, object );
 
-    projection_list := List( [ 1 .. nr_summands ], i -> ProjectionInFactorOfDirectSum( summands, i ) );
+    projection_list := List( [ 1 .. nr_summands ], i -> ProjectionInFactorOfDirectSum( cat, summands, i ) );
 
-    projection_list := List( projection_list, mor -> TensorProductOnMorphisms( id, mor ) );
+    projection_list := List( projection_list, mor -> TensorProductOnMorphisms( cat, id, mor ) );
 
-    diagram := List( summands, summand -> TensorProductOnObjects( object, summand ) );
+    diagram := List( summands, summand -> TensorProductOnObjects( cat, object, summand ) );
 
-    return UniversalMorphismIntoDirectSum( diagram, projection_list );
+    return UniversalMorphismIntoDirectSum( cat, diagram, projection_list );
 
 end : CategoryFilter := IsMonoidalCategory and IsAdditiveCategory,
       Description := "LeftDistributivityExpandingWithGivenObjects using the universal property of the direct sum" );
@@ -27,15 +27,15 @@ AddDerivationToCAP( LeftDistributivityFactoringWithGivenObjects,
 
     nr_summands := Size( summands );
 
-    id := IdentityMorphism( object );
+    id := IdentityMorphism( cat, object );
 
-    injection_list := List( [ 1 .. nr_summands ], i -> InjectionOfCofactorOfDirectSum( summands, i ) );
+    injection_list := List( [ 1 .. nr_summands ], i -> InjectionOfCofactorOfDirectSum( cat, summands, i ) );
 
-    injection_list := List( injection_list, mor -> TensorProductOnMorphisms( id, mor ) );
+    injection_list := List( injection_list, mor -> TensorProductOnMorphisms( cat, id, mor ) );
 
-    diagram := List( summands, summand -> TensorProductOnObjects( object, summand ) );
+    diagram := List( summands, summand -> TensorProductOnObjects( cat, object, summand ) );
 
-    return UniversalMorphismFromDirectSum( diagram, injection_list );
+    return UniversalMorphismFromDirectSum( cat, diagram, injection_list );
 
 end : CategoryFilter := IsMonoidalCategory and IsAdditiveCategory,
       Description := "LeftDistributivityFactoringWithGivenObjects using the universal property of the direct sum" );
@@ -48,15 +48,15 @@ AddDerivationToCAP( RightDistributivityExpandingWithGivenObjects,
 
     nr_summands := Size( summands );
 
-    id := IdentityMorphism( object );
+    id := IdentityMorphism( cat, object );
 
-    projection_list := List( [ 1 .. nr_summands ], i -> ProjectionInFactorOfDirectSum( summands, i ) );
+    projection_list := List( [ 1 .. nr_summands ], i -> ProjectionInFactorOfDirectSum( cat, summands, i ) );
 
-    projection_list := List( projection_list, mor -> TensorProductOnMorphisms( mor, id ) );
+    projection_list := List( projection_list, mor -> TensorProductOnMorphisms( cat, mor, id ) );
 
-    diagram := List( summands, summand -> TensorProductOnObjects( summand, object ) );
+    diagram := List( summands, summand -> TensorProductOnObjects( cat, summand, object ) );
 
-    return UniversalMorphismIntoDirectSum( diagram, projection_list );
+    return UniversalMorphismIntoDirectSum( cat, diagram, projection_list );
 
 end : CategoryFilter := IsMonoidalCategory and IsAdditiveCategory,
       Description := "RightDistributivityExpandingWithGivenObjects using the universal property of the direct sum" );
@@ -69,15 +69,15 @@ AddDerivationToCAP( RightDistributivityFactoringWithGivenObjects,
 
     nr_summands := Size( summands );
 
-    id := IdentityMorphism( object );
+    id := IdentityMorphism( cat, object );
 
-    injection_list := List( [ 1 .. nr_summands ], i -> InjectionOfCofactorOfDirectSum( summands, i ) );
+    injection_list := List( [ 1 .. nr_summands ], i -> InjectionOfCofactorOfDirectSum( cat, summands, i ) );
 
-    injection_list := List( injection_list, mor -> TensorProductOnMorphisms( mor, id ) );
+    injection_list := List( injection_list, mor -> TensorProductOnMorphisms( cat, mor, id ) );
 
-    diagram := List( summands, summand -> TensorProductOnObjects( summand, object ) );
+    diagram := List( summands, summand -> TensorProductOnObjects( cat, summand, object ) );
 
-    return UniversalMorphismFromDirectSum( diagram, injection_list );
+    return UniversalMorphismFromDirectSum( cat, diagram, injection_list );
 
 end : CategoryFilter := IsMonoidalCategory and IsAdditiveCategory,
       Description := "RightDistributivityFactoringWithGivenObjects using the universal property of the direct sum" );

MonoidalCategories/gap/BraidedMonoidalCategories.gi

@@ -4,9 +4,9 @@ AddDerivationToCAP( Braiding,
   function( cat, object_1, object_2 )
     local source_and_range;
 
-    source_and_range := TensorProductOnObjects( object_1, object_2 );
+    source_and_range := TensorProductOnObjects( cat, object_1, object_2 );
 
-    return BraidingWithGivenTensorProducts( source_and_range, object_1, object_2, source_and_range );
+    return BraidingWithGivenTensorProducts( cat, source_and_range, object_1, object_2, source_and_range );
 
 end : CategoryFilter := IsSkeletalCategory,
       Description := "calling the WithGiven operation in a skeletal setting" );
@@ -17,9 +17,9 @@ AddDerivationToCAP( BraidingInverse,
   function( cat, object_1, object_2 )
     local source_and_range;
 
-    source_and_range := TensorProductOnObjects( object_1, object_2 );
+    source_and_range := TensorProductOnObjects( cat, object_1, object_2 );
 
-    return BraidingInverseWithGivenTensorProducts( source_and_range, object_1, object_2, source_and_range );
+    return BraidingInverseWithGivenTensorProducts( cat, source_and_range, object_1, object_2, source_and_range );
 
 end : CategoryFilter := IsSkeletalCategory,
       Description := "calling the WithGiven operation in a skeletal setting" );

MonoidalCategories/gap/BraidedMonoidalCategoriesDerivedMethods.gi

@@ -3,7 +3,7 @@ AddDerivationToCAP( BraidingInverseWithGivenTensorProducts,
 
   function( cat, object_2_tensored_object_1, object_1, object_2, object_1_tensored_object_2 )
     ##TODO: Use BraidingWithGiven
-    return Inverse( Braiding( object_1, object_2 ) );
+    return InverseForMorphisms( cat, Braiding( cat, object_1, object_2 ) );
 
 end : CategoryFilter := IsBraidedMonoidalCategory,
       Description := "BraidingInverseWithGivenTensorProducts as the inverse of the braiding" );
@@ -13,7 +13,7 @@ AddDerivationToCAP( BraidingWithGivenTensorProducts,
 
   function( cat, object_1_tensored_object_2, object_1, object_2, object_2_tensored_object_1 )
     ##TODO: Use BraidingInverseWithGiven
-    return Inverse( BraidingInverse( object_1, object_2 ) );
+    return InverseForMorphisms( cat, BraidingInverse( cat, object_1, object_2 ) );
 
 end : CategoryFilter := IsBraidedMonoidalCategory,
       Description := "BraidingWithGivenTensorProducts as the inverse of BraidingInverse" );

MonoidalCategories/gap/BraidedMonoidalCategoriesMethodRecord.gi

@@ -3,8 +3,8 @@ InstallValue( BRAIDED_MONOIDAL_CATEGORIES_METHOD_NAME_RECORD, rec(
 Braiding := rec(
   filter_list := [ "category", "object", "object" ],
   io_type := [ [ "a", "b" ], [ "s", "r" ] ],
-  output_source_getter_string := "TensorProductOnObjects( a, b )",
-  output_range_getter_string := "TensorProductOnObjects( b, a )",
+  output_source_getter_string := "TensorProductOnObjects( cat, a, b )",
+  output_range_getter_string := "TensorProductOnObjects( cat, b, a )",
   with_given_object_position := "both",
   return_type := "morphism" ),
 
@@ -16,8 +16,8 @@ BraidingWithGivenTensorProducts := rec(
 BraidingInverse := rec(
   filter_list := [ "category", "object", "object" ],
   io_type := [ [ "a", "b" ], [ "s", "r" ] ],
-  output_source_getter_string := "TensorProductOnObjects( b, a )",
-  output_range_getter_string := "TensorProductOnObjects( a, b )",
+  output_source_getter_string := "TensorProductOnObjects( cat, b, a )",
+  output_range_getter_string := "TensorProductOnObjects( cat, a, b )",
   with_given_object_position := "both",
   return_type := "morphism" ),
 

MonoidalCategories/gap/ClosedMonoidalCategories.gi

@@ -3,7 +3,7 @@ AddDerivationToCAP( IsomorphismFromInternalHomToObject,
 
   function( cat, object )
 
-    return IsomorphismFromInternalHomToObjectWithGivenInternalHom( object, object );
+    return IsomorphismFromInternalHomToObjectWithGivenInternalHom( cat, object, object );
 
 end : CategoryFilter := IsSkeletalCategory,
       Description := "calling the WithGiven operation in a skeletal setting" );
@@ -13,7 +13,7 @@ AddDerivationToCAP( IsomorphismFromObjectToInternalHom,
 
   function( cat, object )
 
-    return IsomorphismFromObjectToInternalHomWithGivenInternalHom( object, object );
+    return IsomorphismFromObjectToInternalHomWithGivenInternalHom( cat, object, object );
 
 end : CategoryFilter := IsSkeletalCategory,
       Description := "calling the WithGiven operation in a skeletal setting" );

MonoidalCategories/gap/ClosedMonoidalCategoriesDerivedMethods.gi

@@ -18,11 +18,8 @@ AddFinalDerivation( IsomorphismFromDualToInternalHom,
                       MorphismFromTensorProductToInternalHomWithGivenObjects ],
 
   function( cat, object )
-    local category;
 
-    category := CapCategory( object );
-    
-    return IdentityMorphism( InternalHomOnObjects( object, TensorUnit( category ) ) );
+    return IdentityMorphism( cat, InternalHomOnObjects( cat, object, TensorUnit( cat ) ) );
 
 end : CategoryFilter := IsClosedMonoidalCategory,
       Description := "IsomorphismFromDualToInternalHom as the identity of Hom(a,1)" );
@@ -42,11 +39,8 @@ AddFinalDerivation( IsomorphismFromInternalHomToDual,
                       MorphismFromTensorProductToInternalHomWithGivenObjects ],
 
   function( cat, object )
-    local category;
-    
-    category := CapCategory( object );
 
-    return IdentityMorphism( InternalHomOnObjects( object, TensorUnit( category ) ) );
+    return IdentityMorphism( cat, InternalHomOnObjects( cat, object, TensorUnit( cat ) ) );
 
 end : CategoryFilter := IsClosedMonoidalCategory,
       Description := "IsomorphismFromInternalHomToDual as the identity of Hom(a,1)" );