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# SPDX-License-Identifier: GPL-2.0-or-later
# GeneralizedMorphismsForCAP: Implementations of generalized morphisms for the CAP project
#
# Implementations
#
## @Chapter Serre Quotients Functors
InstallMethod( SerreQuotientConversionFunctor,
[ IsCapCategory and WasCreatedAsSerreQuotientCategoryByCospans,
IsCapCategory and WasCreatedAsSerreQuotientCategoryByThreeArrows ],
function( source_cat, range_cat )
local functor, generalized_morphism_functor;
if not IsIdenticalObj( UnderlyingHonestCategory( source_cat ), UnderlyingHonestCategory( range_cat ) ) then
Error( "underlying honest categories are not identical" );
fi;
generalized_morphism_functor := FunctorFromCospansToThreeArrows( UnderlyingHonestCategory( source_cat ) );
functor := CapFunctor( Concatenation( "Conversion functor between ", Name( source_cat ), " and ", Name( range_cat ) ),
source_cat,
range_cat );
AddObjectFunction( functor, i -> AsSerreQuotientCategoryByThreeArrowsObject( range_cat, UnderlyingHonestObject( i ) ) );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local new_generalized;
new_generalized := ApplyFunctor( generalized_morphism_functor, UnderlyingGeneralizedMorphism( morphism ) );
return SerreQuotientCategoryByThreeArrowsMorphism( range_cat, new_generalized );
end );
return functor;
end );
InstallMethod( SerreQuotientConversionFunctor,
[ IsCapCategory and WasCreatedAsSerreQuotientCategoryByCospans,
IsCapCategory and WasCreatedAsSerreQuotientCategoryBySpans ],
function( source_cat, range_cat )
local functor, generalized_morphism_functor;
if not IsIdenticalObj( UnderlyingHonestCategory( source_cat ), UnderlyingHonestCategory( range_cat ) ) then
Error( "underlying honest categories are not identical" );
fi;
generalized_morphism_functor := FunctorFromCospansToSpans( UnderlyingHonestCategory( source_cat ) );
functor := CapFunctor( Concatenation( "Conversion functor between ", Name( source_cat ), " and ", Name( range_cat ) ),
source_cat,
range_cat );
AddObjectFunction( functor, i -> AsSerreQuotientCategoryBySpansObject( range_cat, UnderlyingHonestObject( i ) ) );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local new_generalized;
new_generalized := ApplyFunctor( generalized_morphism_functor, UnderlyingGeneralizedMorphism( morphism ) );
return SerreQuotientCategoryBySpansMorphism( range_cat, new_generalized );
end );
return functor;
end );
InstallMethod( SerreQuotientConversionFunctor,
[ IsCapCategory and WasCreatedAsSerreQuotientCategoryBySpans,
IsCapCategory and WasCreatedAsSerreQuotientCategoryByThreeArrows ],
function( source_cat, range_cat )
local functor, generalized_morphism_functor;
if not IsIdenticalObj( UnderlyingHonestCategory( source_cat ), UnderlyingHonestCategory( range_cat ) ) then
Error( "underlying honest categories are not identical" );
fi;
generalized_morphism_functor := FunctorFromSpansToThreeArrows( UnderlyingHonestCategory( source_cat ) );
functor := CapFunctor( Concatenation( "Conversion functor between ", Name( source_cat ), " and ", Name( range_cat ) ),
source_cat,
range_cat );
AddObjectFunction( functor, i -> AsSerreQuotientCategoryByThreeArrowsObject( range_cat, UnderlyingHonestObject( i ) ) );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local new_generalized;
new_generalized := ApplyFunctor( generalized_morphism_functor, UnderlyingGeneralizedMorphism( morphism ) );
return SerreQuotientCategoryByThreeArrowsMorphism( range_cat, new_generalized );
end );
return functor;
end );
InstallMethod( SerreQuotientConversionFunctor,
[ IsCapCategory and WasCreatedAsSerreQuotientCategoryByThreeArrows,
IsCapCategory and WasCreatedAsSerreQuotientCategoryBySpans ],
function( source_cat, range_cat )
local functor, generalized_morphism_functor;
if not IsIdenticalObj( UnderlyingHonestCategory( source_cat ), UnderlyingHonestCategory( range_cat ) ) then
Error( "underlying honest categories are not identical" );
fi;
generalized_morphism_functor := FunctorFromThreeArrowsToSpans( UnderlyingHonestCategory( source_cat ) );
functor := CapFunctor( Concatenation( "Conversion functor between ", Name( source_cat ), " and ", Name( range_cat ) ),
source_cat,
range_cat );
AddObjectFunction( functor, i -> AsSerreQuotientCategoryBySpansObject( range_cat, UnderlyingHonestObject( i ) ) );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local new_generalized;
new_generalized := ApplyFunctor( generalized_morphism_functor, UnderlyingGeneralizedMorphism( morphism ) );
return SerreQuotientCategoryBySpansMorphism( range_cat, new_generalized );
end );
return functor;
end );
InstallMethod( SerreQuotientConversionFunctor,
[ IsCapCategory and WasCreatedAsSerreQuotientCategoryByThreeArrows,
IsCapCategory and WasCreatedAsSerreQuotientCategoryByCospans ],
function( source_cat, range_cat )
local functor, generalized_morphism_functor;
if not IsIdenticalObj( UnderlyingHonestCategory( source_cat ), UnderlyingHonestCategory( range_cat ) ) then
Error( "underlying honest categories are not identical" );
fi;
generalized_morphism_functor := FunctorFromThreeArrowsToCospans( UnderlyingHonestCategory( source_cat ) );
functor := CapFunctor( Concatenation( "Conversion functor between ", Name( source_cat ), " and ", Name( range_cat ) ),
source_cat,
range_cat );
AddObjectFunction( functor, i -> AsSerreQuotientCategoryByCospansObject( range_cat, UnderlyingHonestObject( i ) ) );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local new_generalized;
new_generalized := ApplyFunctor( generalized_morphism_functor, UnderlyingGeneralizedMorphism( morphism ) );
return SerreQuotientCategoryByCospansMorphism( range_cat, new_generalized );
end );
return functor;
end );
InstallMethod( SerreQuotientConversionFunctor,
[ IsCapCategory and WasCreatedAsSerreQuotientCategoryBySpans,
IsCapCategory and WasCreatedAsSerreQuotientCategoryByCospans ],
function( source_cat, range_cat )
local functor, generalized_morphism_functor;
if not IsIdenticalObj( UnderlyingHonestCategory( source_cat ), UnderlyingHonestCategory( range_cat ) ) then
Error( "underlying honest categories are not identical" );
fi;
generalized_morphism_functor := FunctorFromSpansToCospans( UnderlyingHonestCategory( source_cat ) );
functor := CapFunctor( Concatenation( "Conversion functor between ", Name( source_cat ), " and ", Name( range_cat ) ),
source_cat,
range_cat );
AddObjectFunction( functor, i -> AsSerreQuotientCategoryByCospansObject( range_cat, UnderlyingHonestObject( i ) ) );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local new_generalized;
new_generalized := ApplyFunctor( generalized_morphism_functor, UnderlyingGeneralizedMorphism( morphism ) );
return SerreQuotientCategoryByCospansMorphism( range_cat, new_generalized );
end );
return functor;
end );
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