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products/Sources/formale Sprachen/GAP/pkg/monoidalcategories/gap/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 25.7.2025 mit Größe 2 kB

Quelle AdditiveMonoidalCategories.gi Sprache: unbekannt

# SPDX-License-Identifier: GPL-2.0-or-later
# MonoidalCategories: Monoidal and monoidal (co)closed categories
#
# Implementations
#

##
AddDerivationToCAP( LeftDistributivityExpanding,
                    "calling the WithGiven operation in a skeletal setting",
                    [ [ TensorProductOnObjects, 1 ],
                      [ DirectSum, 1 ],
                      [ LeftDistributivityExpandingWithGivenObjects, 1 ] ],

  function( cat, object, summands_list )
    local source_and_range;

    source_and_range := TensorProductOnObjects( cat, object, DirectSum( cat, summands_list ) );

    return LeftDistributivityExpandingWithGivenObjects( cat,
             source_and_range,
             object, summands_list,
             source_and_range
           );

end : CategoryFilter := IsSkeletalCategory );

##
AddDerivationToCAP( LeftDistributivityFactoring,
                    "calling the WithGiven operation in a skeletal setting",
                    [ [ TensorProductOnObjects, 1 ],
                      [ DirectSum, 1 ],
                      [ LeftDistributivityFactoringWithGivenObjects, 1 ] ],

  function( cat, object, summands_list )
    local source_and_range;

    source_and_range := TensorProductOnObjects( cat, object, DirectSum( cat, summands_list ) );

    return LeftDistributivityFactoringWithGivenObjects( cat,
             source_and_range,
             object, summands_list,
             source_and_range
           );

end : CategoryFilter := IsSkeletalCategory );

##
AddDerivationToCAP( RightDistributivityExpanding,
                    "calling the WithGiven operation in a skeletal setting",
                    [ [ TensorProductOnObjects, 1 ],
                      [ DirectSum, 1 ],
                      [ RightDistributivityExpandingWithGivenObjects, 1 ] ],

  function( cat, summands_list, object )
    local source_and_range;

    source_and_range := TensorProductOnObjects( cat, DirectSum( cat, summands_list ), object );

    return RightDistributivityExpandingWithGivenObjects( cat,
             source_and_range,
             summands_list, object,
             source_and_range
           );

end : CategoryFilter := IsSkeletalCategory );

##
AddDerivationToCAP( RightDistributivityFactoring,
                    "calling the WithGiven operation in a skeletal setting",
                    [ [ TensorProductOnObjects, 1 ],
                      [ DirectSum, 1 ],
                      [ RightDistributivityFactoringWithGivenObjects, 1 ] ],

  function( cat, summands_list, object )
    local source_and_range;

    source_and_range := TensorProductOnObjects( cat, DirectSum( cat, summands_list ), object );

    return RightDistributivityFactoringWithGivenObjects( cat,
             source_and_range,
             summands_list, object,
             source_and_range
           );

end : CategoryFilter := IsSkeletalCategory );