CAP_project/MonoidalCategories/gap/SymmetricMonoidalCategoriesDerivedMethods.gi at 8b5ad6b8eb15c655b15fc3847ba8893d8ef1c920 · mohamed-barakat/CAP_project · GitHub

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# SPDX-License-Identifier: GPL-2.0-or-later
# MonoidalCategories: Monoidal and monoidal (co)closed categories
#
# 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",
                    [ [ BraidingInverseWithGivenTensorProducts, 1 ] ],

  function( cat, object_1_tensored_object_2, object_1, object_2, object_2_tensored_object_1 )

    return BraidingInverseWithGivenTensorProducts( cat,
                            object_1_tensored_object_2,
                            object_2, object_1,
                            object_2_tensored_object_1 );

end : CategoryFilter := IsSymmetricMonoidalCategory );

##
AddDerivationToCAP( BraidingInverseWithGivenTensorProducts,
                    "BraidingInverseWithGivenTensorProducts using BraidingWithGivenTensorProducts",
                    [ [ BraidingWithGivenTensorProducts, 1 ] ],

  function( cat, object_2_tensored_object_1, object_1, object_2, object_1_tensored_object_2 )

    return BraidingWithGivenTensorProducts( cat,
                     object_2_tensored_object_1,
                     object_2, object_1,
                     object_1_tensored_object_2 );

end : CategoryFilter := IsSymmetricMonoidalCategory );