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# SPDX-License-Identifier: GPL-2.0-or-later
# MonoidalCategories: Monoidal and monoidal (co)closed categories
#
# Implementations
#
##
AddDerivationToCAP( IsomorphismFromInternalHomToObject,
"calling the WithGiven operation in a skeletal setting",
[ [ IsomorphismFromInternalHomToObjectWithGivenInternalHom, 1 ] ],
function( cat, object )
return IsomorphismFromInternalHomToObjectWithGivenInternalHom( cat, object, object );
end : CategoryFilter := IsSkeletalCategory );
##
AddDerivationToCAP( IsomorphismFromObjectToInternalHom,
"calling the WithGiven operation in a skeletal setting",
[ [ IsomorphismFromObjectToInternalHomWithGivenInternalHom, 1 ] ],
function( cat, object )
return IsomorphismFromObjectToInternalHomWithGivenInternalHom( cat, object, object );
end : CategoryFilter := IsSkeletalCategory );
####################################
# Convenience Methods
####################################
##
InstallMethod( InternalHom,
[ IsCapCategoryObject, IsCapCategoryObject ],
InternalHomOnObjects );
##
InstallMethod( InternalHom,
[ IsCapCategoryMorphism, IsCapCategoryMorphism ],
InternalHomOnMorphisms );
##
InstallMethod( InternalHom,
[ IsCapCategoryObject, IsCapCategoryMorphism ],
function( a, beta )
return InternalHomOnMorphisms( IdentityMorphism( a ), beta );
end );
##
InstallMethod( InternalHom,
[ IsCapCategoryMorphism, IsCapCategoryObject ],
function( alpha, b )
return InternalHomOnMorphisms( alpha, IdentityMorphism( b ) );
end );
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