|
# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Implementations
#
InstallTrueMethod( IsDiscreteCategory, IsTerminalCategory );
####################################
#
# Constructor
#
####################################
##
InstallGlobalFunction( FiniteSkeletalDiscreteCategory,
FunctionWithNamedArguments(
[
[ "FinalizeCategory", true ],
],
function( CAP_NAMED_ARGUMENTS, list_of_gap_objects )
local name, D;
name := Concatenation( "FiniteSkeletalDiscreteCategory( ", String( list_of_gap_objects ), " )" );
D := CreateCapCategoryWithDataTypes( name,
IsFiniteSkeletalDiscreteCategory,
IsObjectInFiniteSkeletalDiscreteCategory,
IsMorphismInFiniteSkeletalDiscreteCategory,
IsCapCategoryTwoCell,
rec( category := false,
filter := IsObject ),
fail,
fail );
D!.compiler_hints := rec( category_attribute_names := [ "UnderlyingListOfGapObjects" ] );
SetUnderlyingListOfGapObjects( D, list_of_gap_objects );
SetIsFiniteCategory( D, true );
SetIsSkeletalCategory( D, true );
SetIsDiscreteCategory( D, true );
####################################
#
# Primitive operations
#
####################################
##
AddObjectConstructor( D,
function( D, gap_object )
#% CAP_JIT_DROP_NEXT_STATEMENT
Assert( 0, gap_object in UnderlyingListOfGapObjects( D ) );
return CreateCapCategoryObjectWithAttributes( D,
UnderlyingGapObject, gap_object );
end );
##
AddObjectDatum( D,
function( D, object )
return UnderlyingGapObject( object );
end );
##
AddMorphismConstructor( D,
function( D, source, m, target )
#% CAP_JIT_DROP_NEXT_STATEMENT
Assert( 0, IsEqualForObjects( D, source, target ) );
return CreateCapCategoryMorphismWithAttributes( D, source, target );
end );
##
AddMorphismDatum( D,
function( D, morphism )
return fail;
end );
##
AddIsWellDefinedForObjects( D,
function( D, object )
return UnderlyingGapObject( object ) in UnderlyingListOfGapObjects( D );
end );
##
AddIsWellDefinedForMorphisms( D,
function( D, morphism )
return IsEndomorphism( D, morphism ) and IsOne( D, morphism );
end );
AddIsEqualForObjects( D,
function( D, object_1, object_2 )
return UnderlyingGapObject( object_1 ) = UnderlyingGapObject( object_2 );
end );
##
AddIsEqualForMorphisms( D,
function( D, morphism_1, morphism_2 )
return true;
end );
##
AddIdentityMorphism( D,
function( D, object )
return MorphismConstructor( D, object, fail, object );
end );
##
AddPreCompose( D,
function( D, morphism_1, morphism_2 )
return morphism_1;
end );
##
AddSetOfObjectsOfCategory( D,
function( D )
return List( UnderlyingListOfGapObjects( D ), obj -> ObjectConstructor( D, obj ) );
end );
##
AddSetOfMorphismsOfFiniteCategory( D,
function( D )
return List( SetOfObjectsOfCategory( D ), obj -> IdentityMorphism( D, obj ) );
end );
if CAP_NAMED_ARGUMENTS.FinalizeCategory then
Finalize( D );
fi;
return D;
end ) );
#################################
#
# Operators
#
#################################
##
InstallOtherMethod( \[\],
"for a finite skeletal discrete category and a positive integer",
[ IsFiniteSkeletalDiscreteCategory, IsInt ],
function ( D, index )
local objects;
objects := SetOfObjectsOfCategory( D );
if index <= 0 or index > Length( objects ) then
# COVERAGE_IGNORE_NEXT_LINE
Error( "out of bounds access\n" );
fi;
return objects[index];
end );
#################################
#
# View & Display
#
#################################
##
InstallMethod( DisplayString,
[ IsObjectInFiniteSkeletalDiscreteCategory ],
function( object )
return Concatenation( String( UnderlyingGapObject( object ) ), "\n" );
end );
##
InstallMethod( DisplayString,
[ IsMorphismInFiniteSkeletalDiscreteCategory ],
function( morphism )
return Concatenation( DisplayString( Source( morphism ) ),
"|\n| ",
String( morphism ),
"\nv\n",
DisplayString( Target( morphism ) ) );
end );
[ Verzeichnis aufwärts0.37unsichere Verbindung
Übersetzung europäischer Sprachen durch Browser
]
|
