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LoadPackage( "CAP" );
DeclareCategory( "IsCategoryOfHomalgIntegers",
IsCapCategory );
DeclareCategory( "IsObjectInCategoryOfHomalgIntegers",
IsCapCategoryObject );
DeclareCategory( "IsMorphismInCategoryOfHomalgIntegers",
IsCapCategoryMorphism );
############################
##
## Attributes
##
############################
DeclareAttribute( "UnderlyingInteger",
IsObjectInCategoryOfHomalgIntegers );
############################
##
## Category
##
############################
integer_category := CreateCapCategory( "HomalgIntegers",
IsCategoryOfHomalgIntegers,
IsObjectInCategoryOfHomalgIntegers,
IsMorphismInCategoryOfHomalgIntegers,
IsCapCategoryTwoCell );
#############################
##
## Constructors
##
#############################
DeclareOperation( "HomalgInteger",
[ IsInt ] );
##
InstallMethodWithCache( HomalgInteger,
[ IsInt ],
function( integer )
return CreateCapCategoryObjectWithAttributes( integer_category,
UnderlyingInteger, integer );
end );
DeclareOperation( "HomalgIntegerMorphism",
[ IsInt, IsInt ] );
##
InstallMethod( HomalgIntegerMorphism,
[ IsInt, IsInt ],
function( source, range )
return HomalgIntegerMorphism( HomalgInteger( source ), HomalgInteger( range ) );
end );
DeclareOperation( "HomalgIntegerMorphism",
[ IsObjectInCategoryOfHomalgIntegers, IsObjectInCategoryOfHomalgIntegers ] );
##
InstallMethodWithCache( HomalgIntegerMorphism,
[ IsObjectInCategoryOfHomalgIntegers, IsObjectInCategoryOfHomalgIntegers ],
function( source, range )
if UnderlyingInteger( range ) < UnderlyingInteger( source ) then
Error( "such a morphism does not exist" );
fi;
return CreateCapCategoryMorphismWithAttributes( integer_category,
source,
range );
end );
##
AddIsCongruentForMorphisms( integer_category,
function( cat, mor1, mor2 )
return true;
end );
##
AddIsZeroForMorphisms( integer_category,
function( cat, a )
return true;
end );
##
AddAdditionForMorphisms( integer_category,
function( cat, a, b )
return a;
end );
##
AddAdditiveInverseForMorphisms( integer_category,
function( cat, mor )
return mor;
end );
##
AddZeroMorphism( integer_category,
function( cat, a, b )
return HomalgIntegerMorphism( a, b );
end );
##
AddIdentityMorphism( integer_category,
function( cat, obj )
return HomalgIntegerMorphism( obj, obj );
end );
##
AddPreCompose( integer_category,
function( cat, mor1, mor2 )
return HomalgIntegerMorphism( Source( mor1 ), Range( mor2 ) );
end );
#
AddFiberProduct( integer_category,
function( cat, product_mor )
local pullback;
pullback := Gcd( List( product_mor, i -> UnderlyingInteger( Source( i ) ) ) );
return HomalgInteger( pullback );
end );
##
AddProjectionInFactorOfFiberProductWithGivenFiberProduct( integer_category,
function( cat, product_morx, coordinate, pullback )
local range;
range := Source( product_morx[ coordinate ] );
return HomalgIntegerMorphism( pullback, range );
end );
##
AddPushout( integer_category,
function( cat, product_mor )
local pushout;
pushout := Lcm( List( product_mor, i -> UnderlyingInteger( Range( i ) ) ) );
return HomalgInteger( pushout );
end );
##
AddInjectionOfCofactorOfPushoutWithGivenPushout( integer_category,
function( cat, product_mor, coordinate, pushout )
local source;
source := Range( product_mor[ coordinate ] );
return HomalgIntegerMorphism( source, pushout );
end );
##
AddLiftAlongMonomorphism( integer_category,
function( cat, monomorphism, test_morphism )
return HomalgIntegerMorphism( Source( test_morphism ), Source( monomorphism ) );
end );
###################################
##
## View
##
###################################
##
InstallMethod( ViewString,
[ IsObjectInCategoryOfHomalgIntegers ],
function( integer_obj )
return Concatenation( "<The integer object representing ", String( UnderlyingInteger( integer_obj ) ), ">" );
end );
##
InstallMethod( ViewString,
[ IsMorphismInCategoryOfHomalgIntegers ],
function( integer_mor )
return Concatenation( "<", String( UnderlyingInteger( Source( integer_mor ) ) ), " -> ", String( UnderlyingInteger( Range( integer_mor ) ) ), ">" );
end );
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