diff --git a/CartesianCategories/PackageInfo.g b/CartesianCategories/PackageInfo.g
index 1021dd6ff9..187623382e 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 := "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 := [ ],
diff --git a/CartesianCategories/gap/AUTOGENERATED_FROM.md b/CartesianCategories/gap/AUTOGENERATED_FROM.md
index bb76fcecb4..101cb07872 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 v2026.08-01
+* from MonoidalCategories v2026.08-02
diff --git a/CartesianCategories/gap/SymmetricCartesianCategoriesDerivedMethods.gi b/CartesianCategories/gap/SymmetricCartesianCategoriesDerivedMethods.gi
index 3e892289b8..ee82a7bcae 100644
--- a/CartesianCategories/gap/SymmetricCartesianCategoriesDerivedMethods.gi
+++ b/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",
diff --git a/CartesianCategories/gap/SymmetricCocartesianCategoriesDerivedMethods.gi b/CartesianCategories/gap/SymmetricCocartesianCategoriesDerivedMethods.gi
index be83e64305..7f3d353a25 100644
--- a/CartesianCategories/gap/SymmetricCocartesianCategoriesDerivedMethods.gi
+++ b/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",
diff --git a/MonoidalCategories/PackageInfo.g b/MonoidalCategories/PackageInfo.g
index 5bf661b300..1fa529eb75 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 := "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",
 
diff --git a/MonoidalCategories/gap/SymmetricMonoidalCategoriesDerivedMethods.gi b/MonoidalCategories/gap/SymmetricMonoidalCategoriesDerivedMethods.gi
index 8aa732484e..f1144871e3 100644
--- a/MonoidalCategories/gap/SymmetricMonoidalCategoriesDerivedMethods.gi
+++ b/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",
diff --git a/MonoidalCategories/gap/SymmetricMonoidalCategoriesProperties.gi b/MonoidalCategories/gap/SymmetricMonoidalCategoriesProperties.gi
index 67221e2fff..0aa5bed2d0 100644
--- a/MonoidalCategories/gap/SymmetricMonoidalCategoriesProperties.gi
+++ b/MonoidalCategories/gap/SymmetricMonoidalCategoriesProperties.gi
@@ -5,6 +5,6 @@
 #
 
 CAP_INTERNAL_CONSTRUCTIVE_CATEGORIES_RECORD.IsSymmetricMonoidalCategory :=
-  ListOfDefiningOperations( "IsBraidedMonoidalCategory" );
+  Difference( ListOfDefiningOperations( "IsBraidedMonoidalCategory" ), [ "BraidingInverse" ] );
 
 InstallTrueMethod( IsBraidedMonoidalCategory, IsSymmetricMonoidalCategory );