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# SPDX-License-Identifier: GPL-2.0-or-later
# MonoidalCategories: Monoidal and monoidal (co)closed categories
#
# Implementations
#
InstallTrueMethod( IsMonoidalCategory, IsStrictMonoidalCategory );
##
AddDerivationToCAP( AssociatorRightToLeft,
"calling the WithGiven operation in a skeletal setting",
[ [ TensorProductOnObjects, 2 ],
[ AssociatorRightToLeftWithGivenTensorProducts, 1 ] ],
function( cat, object_1, object_2, object_3 )
local source_and_range;
source_and_range := TensorProductOnObjects( cat, object_1, TensorProductOnObjects( cat, object_2, object_3 ) );
return AssociatorRightToLeftWithGivenTensorProducts( cat,
source_and_range,
object_1, object_2, object_3,
source_and_range
);
end : CategoryFilter := IsSkeletalCategory );
##
AddDerivationToCAP( AssociatorLeftToRight,
"calling the WithGiven operation in a skeletal setting",
[ [ TensorProductOnObjects, 2 ],
[ AssociatorLeftToRightWithGivenTensorProducts, 1 ] ],
function( cat, object_1, object_2, object_3 )
local source_and_range;
source_and_range := TensorProductOnObjects( cat, object_1, TensorProductOnObjects( cat, object_2, object_3 ) );
return AssociatorLeftToRightWithGivenTensorProducts( cat,
source_and_range,
object_1, object_2, object_3,
source_and_range
);
end : CategoryFilter := IsSkeletalCategory );
##
AddDerivationToCAP( LeftUnitor,
"calling the WithGiven operation in a skeletal setting",
[ [ LeftUnitorWithGivenTensorProduct, 1 ] ],
function( cat, object )
return LeftUnitorWithGivenTensorProduct( cat, object, object );
end : CategoryFilter := IsSkeletalCategory );
##
AddDerivationToCAP( LeftUnitorInverse,
"calling the WithGiven operation in a skeletal setting",
[ [ LeftUnitorInverseWithGivenTensorProduct, 1 ] ],
function( cat, object )
return LeftUnitorInverseWithGivenTensorProduct( cat, object, object );
end : CategoryFilter := IsSkeletalCategory );
##
AddDerivationToCAP( RightUnitor,
"calling the WithGiven operation in a skeletal setting",
[ [ RightUnitorWithGivenTensorProduct, 1 ] ],
function( cat, object )
return RightUnitorWithGivenTensorProduct( cat, object, object );
end : CategoryFilter := IsSkeletalCategory );
##
AddDerivationToCAP( RightUnitorInverse,
"calling the WithGiven operation in a skeletal setting",
[ [ RightUnitorInverseWithGivenTensorProduct, 1 ] ],
function( cat, object )
return RightUnitorInverseWithGivenTensorProduct( cat, object, object );
end : CategoryFilter := IsSkeletalCategory );
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