two derivations for symmetric monoidal categories

CartesianCategories/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "CartesianCategories",
 Subtitle := "Cartesian and cocartesian categories and various subdoctrines",
-Version := "2026.08-01",
+Version := "2026.08-02",
 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",
@@ -99,7 +99,7 @@ Dependencies := rec(
   GAP := ">= 4.13.0",
   NeededOtherPackages := [
                 [ "CAP", ">= 2026.06-01" ],
-                [ "MonoidalCategories", ">= 2026.08-01" ],
+                [ "MonoidalCategories", ">= 2026.08-02" ],
                 ],
   SuggestedOtherPackages := [ ],
   ExternalConditions := [ ],

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 v2026.08-01
+* from MonoidalCategories v2026.08-02

CartesianCategories/gap/SymmetricCartesianCategoriesDerivedMethods.gi

@@ -7,6 +7,30 @@
 
 
 
+##
+AddDerivationToCAP( CartesianBraiding,
+                    "CartesianBraiding using CartesianBraidingInverse",
+                    [ [ CartesianBraidingInverse, 1 ] ],
+
+  function( cat, object_1, object_2 )
+
+    return CartesianBraidingInverse( cat,
+                            object_2, object_1 );
+
+end : CategoryFilter := IsCartesianCategory );
+
+##
+AddDerivationToCAP( CartesianBraidingInverse,
+                    "CartesianBraidingInverse using CartesianBraiding",
+                    [ [ CartesianBraiding, 1 ] ],
+
+  function( cat, object_1, object_2 )
+
+    return CartesianBraiding( cat,
+                     object_2, object_1 );
+
+end : CategoryFilter := IsCartesianCategory );
+
 ##
 AddDerivationToCAP( CartesianBraidingWithGivenDirectProducts,
                     "CartesianBraidingWithGivenDirectProducts using CartesianBraidingInverseWithGivenDirectProducts",

CartesianCategories/gap/SymmetricCocartesianCategoriesDerivedMethods.gi

@@ -7,6 +7,30 @@
 
 
 
+##
+AddDerivationToCAP( CocartesianBraiding,
+                    "CocartesianBraiding using CocartesianBraidingInverse",
+                    [ [ CocartesianBraidingInverse, 1 ] ],
+
+  function( cat, object_1, object_2 )
+
+    return CocartesianBraidingInverse( cat,
+                            object_2, object_1 );
+
+end : CategoryFilter := IsCocartesianCategory );
+
+##
+AddDerivationToCAP( CocartesianBraidingInverse,
+                    "CocartesianBraidingInverse using CocartesianBraiding",
+                    [ [ CocartesianBraiding, 1 ] ],
+
+  function( cat, object_1, object_2 )
+
+    return CocartesianBraiding( cat,
+                     object_2, object_1 );
+
+end : CategoryFilter := IsCocartesianCategory );
+
 ##
 AddDerivationToCAP( CocartesianBraidingWithGivenCoproducts,
                     "CocartesianBraidingWithGivenCoproducts using CocartesianBraidingInverseWithGivenCoproducts",

MonoidalCategories/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "MonoidalCategories",
 Subtitle := "Monoidal and monoidal (co)closed categories",
-Version := "2026.08-01",
+Version := "2026.08-02",
 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",
 

MonoidalCategories/gap/SymmetricMonoidalCategoriesDerivedMethods.gi

@@ -4,6 +4,30 @@
 # Implementations
 #
 
+##
+AddDerivationToCAP( Braiding,
+                    "Braiding using BraidingInverse",
+                    [ [ BraidingInverse, 1 ] ],
+
+  function( cat, object_1, object_2 )
+
+    return BraidingInverse( cat,
+                            object_2, object_1 );
+
+end : CategoryFilter := IsSymmetricMonoidalCategory );
+
+##
+AddDerivationToCAP( BraidingInverse,
+                    "BraidingInverse using Braiding",
+                    [ [ Braiding, 1 ] ],
+
+  function( cat, object_1, object_2 )
+
+    return Braiding( cat,
+                     object_2, object_1 );
+
+end : CategoryFilter := IsSymmetricMonoidalCategory );
+
 ##
 AddDerivationToCAP( BraidingWithGivenTensorProducts,
                     "BraidingWithGivenTensorProducts using BraidingInverseWithGivenTensorProducts",

MonoidalCategories/gap/SymmetricMonoidalCategoriesProperties.gi

@@ -5,6 +5,6 @@
 #
 
 CAP_INTERNAL_CONSTRUCTIVE_CATEGORIES_RECORD.IsSymmetricMonoidalCategory :=
-  ListOfDefiningOperations( "IsBraidedMonoidalCategory" );
+  Difference( ListOfDefiningOperations( "IsBraidedMonoidalCategory" ), [ "BraidingInverse" ] );
 
 InstallTrueMethod( IsBraidedMonoidalCategory, IsSymmetricMonoidalCategory );