|
# SPDX-License-Identifier: GPL-2.0-or-later
# GeneralizedMorphismsForCAP: Implementations of generalized morphisms for the CAP project
#
# Implementations
#
BindGlobal( "CAP_INTERNAL_FIND_CORRECT_GENERALIZED_CATEGORY_TYPE",
function( category )
if IsBound( category!.generalized_type ) then
return category!.generalized_morphism_standard;
else
return CAP_INTERNAL!.generalized_morphism_standard;
fi;
end );
InstallGlobalFunction( SwitchGeneralizedMorphismStandard,
function( arg )
local string, category;
if Length( arg ) = 1 and IsString( arg[ 1 ] ) then
category := CAP_INTERNAL;
string := arg[ 1 ];
elif Length( arg ) = 2 and IsString( arg[ 1 ] ) and IsCapCategory( arg[ 2 ] ) then
category := arg[ 2 ];
string := arg[ 1 ];
elif Length( arg ) = 2 and IsString( arg[ 2 ] ) and IsCapCategory( arg[ 1 ] ) then
category := arg[ 1 ];
string := arg[ 2 ];
else
Error( "input must be a string or a category and a string" );
return;
fi;
if not string in [ "threearrow", "cospan", "span" ] then
Error( "string must be threearrow, cospan, or span" );
return;
fi;
category!.generalized_morphism_standard := string;
end );
SwitchGeneralizedMorphismStandard( "threearrow" );
InstallValue( CAP_INTERNAL_GENERALIZED_MORPHISM_TRANSLATION_LIST, [
[ "GeneralizedMorphismObject", "GeneralizedMorphismByThreeArrowsObject", "GeneralizedMorphismByCospansObject", "GeneralizedMorphismBySpansObject", [ IsCapCategoryObject ] ],
[ "AsGeneralizedMorphism", "AsGeneralizedMorphismByThreeArrows", "AsGeneralizedMorphismByCospan", "AsGeneralizedMorphismBySpan", [ IsCapCategoryMorphism ] ],
[ "GeneralizedMorphism", "GeneralizedMorphismByThreeArrows", "GeneralizedMorphismByCospan", "GeneralizedMorphismBySpan", [ IsCapCategoryMorphism, IsCapCategoryMorphism ] ],
[ "GeneralizedMorphism", "GeneralizedMorphismByThreeArrows", "GeneralizedMorphismByCospan", "GeneralizedMorphismBySpan", [ IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism ] ],
[ "GeneralizedInverse", "GeneralizedInverseByThreeArrows", "GeneralizedInverseByCospan", "GeneralizedInverseBySpan", [ IsCapCategoryMorphism ] ],
[ "GeneralizedMorphismFromFactorToSubobject", "GeneralizedMorphismFromFactorToSubobjectByThreeArrows", "GeneralizedMorphismFromFactorToSubobjectByCospan", "GeneralizedMorphismFromFactorToSubobjectBySpan", [ IsCapCategoryMorphism, IsCapCategoryMorphism ] ],
[ "IdempotentDefinedBySubobject", "IdempotentDefinedBySubobjectByThreeArrows", "IdempotentDefinedBySubobjectByCospan", "IdempotentDefinedBySubobjectBySpan", [ IsCapCategoryMorphism ] ],
[ "IdempotentDefinedByFactorobject", "IdempotentDefinedByFactorobjectByThreeArrows", "IdempotentDefinedByFactorobjectByCospan", "IdempotentDefinedByFactorobjectBySpan", [ IsCapCategoryMorphism ] ],
[ "GeneralizedMorphismWithRangeAid", "GeneralizedMorphismByThreeArrowsWithRangeAid", "GeneralizedMorphismByCospan", "GeneralizedMorphismBySpanWithRangeAid", [ IsCapCategoryMorphism, IsCapCategoryMorphism ] ],
[ "GeneralizedMorphismWithSourceAid", "GeneralizedMorphismByThreeArrowsWithSourceAid", "GeneralizedMorphismByCospanWithSourceAid", "GeneralizedMorphismBySpan", [ IsCapCategoryMorphism, IsCapCategoryMorphism ] ] ] );
InstallMethod( GeneralizedMorphismCategory,
[ IsCapCategory ],
function( category )
local generalized_type;
generalized_type := CAP_INTERNAL_FIND_CORRECT_GENERALIZED_CATEGORY_TYPE( category );
if generalized_type = "threearrow" then
return GeneralizedMorphismCategoryByThreeArrows( category );
elif generalized_type = "cospan" then
return GeneralizedMorphismCategoryByCospans( category );
elif generalized_type = "span" then
return GeneralizedMorphismCategoryBySpans( category );
else
Error( "generalized morphism type unrecognized" );
fi;
end );
InstallMethod( SerreQuotientCategory,
[ IsCapCategory, IsFunction ],
function( category, func )
local generalized_type;
generalized_type := CAP_INTERNAL_FIND_CORRECT_GENERALIZED_CATEGORY_TYPE( category );
if generalized_type = "threearrow" then
return SerreQuotientCategoryByThreeArrows( category, func );
elif generalized_type = "cospan" then
return SerreQuotientCategoryByCospans( category, func );
elif generalized_type = "span" then
return SerreQuotientCategoryBySpans( category, func );
else
Error( "generalized morphism type unrecognized" );
fi;
end );
BindGlobal( "CAP_INTERNAL_INSTALL_METHODS_FOR_GENERALIZED_MORPHISM_SWITCHER",
function( )
local method_for_switcher, current_method;
method_for_switcher := function( three_arrow, cospan, span )
return function( arg )
local generalized_type;
generalized_type := CAP_INTERNAL_FIND_CORRECT_GENERALIZED_CATEGORY_TYPE( CapCategory( arg[ 1 ] ) );
if generalized_type = "threearrow" then
return CallFuncList( three_arrow, arg );
elif generalized_type = "cospan" then
return CallFuncList( cospan, arg );
elif generalized_type = "span" then
return CallFuncList( span, arg );
else
Error( "generalized morphism type unrecognized" );
fi;
end;
end;
for current_method in CAP_INTERNAL_GENERALIZED_MORPHISM_TRANSLATION_LIST do
InstallMethod( ValueGlobal( current_method[ 1 ] ),
current_method[ 5 ],
method_for_switcher( ValueGlobal( current_method[ 2 ] ), ValueGlobal( current_method[ 3 ] ), ValueGlobal( current_method[ 4 ] ) ) );
od;
end );
CAP_INTERNAL_INSTALL_METHODS_FOR_GENERALIZED_MORPHISM_SWITCHER();
InstallGlobalFunction( "SwitchGeneralizedMorphismStandardHARDCODE",
function( type )
local generalized_morphism_translation_list, i;
if IsString( type ) then
if LowercaseString( type ) = "threearrow" then
type := 2;
elif LowercaseString( type ) = "cospan" then
type := 3;
elif LowercaseString( type ) = "span" then
type := 4;
fi;
fi;
if not IsInt( type ) or not type in [ 2, 3, 4 ] then
Error( "input must be threearrow, cospan, or span" );
fi;
for i in CAP_INTERNAL_GENERALIZED_MORPHISM_TRANSLATION_LIST do
if IsBoundGlobal( i[ 1 ] ) then
MakeReadWriteGlobal( i[ 1 ] );
UnbindGlobal( i[ 1 ] );
fi;
if IsBound( i[ type ] ) then
BindGlobal( i[ 1 ], ValueGlobal( i[ type ] ) );
fi;
od;
end );
[ Verzeichnis aufwärts0.36unsichere Verbindung
Übersetzung europäischer Sprachen durch Browser
]
|
