Quelle  CategoryMorphisms.gi   Sprache: Shell

# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Implementations
#

######################################
##
## Reps, types, stuff.
##
######################################

# backwards compatibility
BindGlobal( "IsCapCategoryMorphismRep", IsCapCategoryMorphism );

#######################################
##
## Technical implications
##
#######################################

InstallValue( PROPAGATION_LIST_FOR_EQUAL_MORPHISMS, [ ] );

##
InstallGlobalFunction( INSTALL_TODO_LIST_FOR_EQUAL_MORPHISMS,
                       
  function( morphism_1, morphism_2 )
    local category, i, entry;
    
    category := CapCategory( morphism_1 );
    
    for i in PROPAGATION_LIST_FOR_EQUAL_MORPHISMS do
        
        AddToToDoList( ToDoListEntryForEqualAttributes( morphism_1, i, morphism_2, i ) );
        
    od;
    
    if IsBound( category!.PROPAGATION_LIST_FOR_EQUAL_MORPHISMS ) then
        
        for i in category!.PROPAGATION_LIST_FOR_EQUAL_MORPHISMS do
            
            AddToToDoList( ToDoListEntryForEqualAttributes( morphism_1, i, morphism_2, i ) );
            
        od;
        
    fi;
    
end );

##
InstallMethod( AddPropertyToMatchAtIsCongruentForMorphisms,
               [ IsCapCategory, IsString ],
               
  function( category, name )
    
    if not IsBound( category!.PROPAGATION_LIST_FOR_EQUAL_MORPHISMS ) then
        
        category!.PROPAGATION_LIST_FOR_EQUAL_MORPHISMS := [ ];
        
    fi;
    
    if Position( category!.PROPAGATION_LIST_FOR_EQUAL_MORPHISMS, name ) = fail then
        
        Add( category!.PROPAGATION_LIST_FOR_EQUAL_MORPHISMS, name );
        
    fi;
    
end );

######################################
##
## Operations
##
######################################

InstallMethod( Target,
               [ IsCapCategoryMorphism ],
               
  Range );

InstallMethod( Add,
               [ IsCapCategory, IsCapCategoryMorphism ],
               
  function( category, morphism )
    local filter;
    
    filter := MorphismFilter( category );
    
    if not filter( morphism ) then
        
        SetFilterObj( morphism, filter );
        
    fi;
    
    if HasCapCategory( morphism ) then
        
        if not IsIdenticalObj( CapCategory( morphism ), category ) then
            
            Error(
                Concatenation(
                    "a morphism that lies in the CAP-category with the name\n",
                    Name( CapCategory( morphism ) ),
                    "\n",
                    "was tried to be added to a different CAP-category with the name\n",
                    Name( category ), ".\n",
                    "(Please note that it is possible for different CAP-categories to have the same name)"
                )
            );
            
        fi;
        
    else
        
        SetCapCategory( morphism, category );
        
    fi;
    
    AddObject( category, Source( morphism ) );
    
    AddObject( category, Range( morphism ) );
    
    if category!.predicate_logic then
        
        INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Source", [ morphism ], Source( morphism ), category );
        
        INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Range", [ morphism ], Range( morphism ), category );
      
    fi;
    
end );

InstallMethod( AddMorphism,
               [ IsCapCategory, IsCapCategoryMorphism ],
               
  function( category, morphism )
    
    Add( category, morphism );
    
end );

InstallMethod( AddMorphism,
               [ IsCapCategory, IsAttributeStoringRep ],
               
  function( category, morphism )
    
    SetFilterObj( morphism, IsCapCategoryMorphism );
    
    Add( category, morphism );
    
end );

##
InstallGlobalFunction( CreateCapCategoryMorphismWithAttributes,
                       
  function( category, source, range, additional_arguments_list... )
    local arg_list, objectified_morphism;
    
    arg_list := Concatenation(
        [ category!.morphism_type, CapCategory, category, Source, source, Range, range ], additional_arguments_list
    );
    
    objectified_morphism := CallFuncList( CreateGapObjectWithAttributes, arg_list );
    
    if category!.predicate_logic then
        INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Source", [ objectified_morphism ], source, category );
        INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Range", [ objectified_morphism ], range, category );
    fi;
    
    return objectified_morphism;
    
end );

##
InstallGlobalFunction( AsCapCategoryMorphism,
                       
  function( category, source, morphism_datum, range )
    local morphism_datum_type, mor;
    
    morphism_datum_type := CAP_INTERNAL_GET_DATA_TYPE_FROM_STRING( "morphism_datum", category );
    
    if morphism_datum_type <> fail then
        
        CAP_INTERNAL_ASSERT_VALUE_IS_OF_TYPE_GETTER( morphism_datum_type, {} -> "the third argument of `AsCapCategoryMorphism`" )( morphism_datum );
        
    fi;
    
    mor := CreateGapObjectWithAttributes( category!.morphism_type, CapCategory, category, Source, source, Range, range, category!.morphism_attribute, morphism_datum );
    
    if not IsIdenticalObj( category!.morphism_attribute( mor ), morphism_datum ) then
        
        Print( "WARNING: <morphism_datum> is not identical to `", category!.morphism_attribute_name, "( <mor> )`. You might want to make <morphism_datum> immutable.\n" );
        
    fi;
    
    if category!.predicate_logic then
        INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Source", [ mor ], source, category );
        INSTALL_TODO_FOR_LOGICAL_THEOREMS( "Range", [ mor ], range, category );
    fi;
    
    return mor;
    
end );

###########################
##
## Print
##
###########################

InstallMethod( String,
               [ IsCapCategoryMorphism ],
               
  function( morphism )
    
    return Concatenation( "A morphism in ", Name( CapCategory( morphism ) ) );
    
end );

# fallback methods for Julia
InstallMethod( ViewString,
               [ IsCapCategoryMorphism ],
               
  function ( morphism )
    
    # do not reuse `String` because morphisms might use `String` as the attribute storing the morphism datum
    return Concatenation( "<A morphism in ", Name( CapCategory( morphism ) ), ">" );
    
end );

InstallMethod( DisplayString,
               [ IsCapCategoryMorphism ],
               
  function ( morphism )
    
    # do not reuse `String` because morphisms might use `String` as the attribute storing the morphism datum
    return Concatenation( "A morphism in ", Name( CapCategory( morphism ) ), ".\n" );
    
end );

##
InstallGlobalFunction( CAP_INTERNAL_CREATE_MORPHISM_PRINT,
                       
  function( )
    local print_graph, morphism_function;
    
    morphism_function := function( object )
      local string;
        
        string := "morphism in ";
        
        Append( string, Name( CapCategory( object ) ) );
        
        return string;
        
    end;
    
    print_graph := CreatePrintingGraph( IsCapCategoryMorphism and HasCapCategory, morphism_function );
    
    AddRelationToGraph( print_graph,
                        rec( Source := [ rec( Conditions := "IsIsomorphism",
                                              PrintString := "iso",
                                              Adjective := true,
                                              NoSepString := true ) ],
                             Range := [ rec( Conditions := "IsSplitMonomorphism",
                                             PrintString := "split mono",
                                             TypeOfView := "ViewObj",
                                             ComputeLevel := "AllWithCompute",
                                             Adjective := true,
                                              NoSepString := true ),
                                        rec( Conditions := "IsSplitEpimorphism",
                                             PrintString := "split epi",
                                             Adjective := true,
                                              NoSepString := true ) ] ) );
    
    AddRelationToGraph( print_graph,
                        rec( Source := [ rec( Conditions := "IsOne",
                                              PrintString := "identity",
                                              Adjective := true ) ],
                             Range := [ rec( Conditions := "IsAutomorphism",
                                             PrintString := "auto",
                                             Adjective := true,
                                             NoSepString := true ),
                                        "IsIsomorphism" ] ) );
    
    AddRelationToGraph( print_graph,
                        rec( Source := [ "IsAutomorphism" ],
                             Range := [ "IsIsomorphism",
                                        rec( Conditions := "IsEndomorphism",
                                             PrintString := "endo",
                                             Adjective := true,
                                             NoSepString := true) ] ) );
    
    AddRelationToGraph( print_graph,
                        rec( Source := [ "IsSplitMonomorphism" ],
                             Range := [ rec( Conditions := "IsMonomorphism",
                                             PrintString := "mono",
                                             Adjective := true,
                                             NoSepString := true ) ] ) );
    
    AddRelationToGraph( print_graph,
                        rec( Source := [ "IsSplitEpimorphism" ],
                             Range := [ rec( Conditions := "IsEpimorphism",
                                             PrintString := "epi",
                                             Adjective := true,
                                             NoSepString := true ) ] ) );
    
    AddNodeToGraph( print_graph,
                    rec( Conditions := "IsZeroForMorphisms",
                         PrintString := "zero",
                         Adjective := true ) );
    
    InstallPrintFunctionsOutOfPrintingGraph( print_graph, -1 );
    
end );

#= comment for Julia
CAP_INTERNAL_CREATE_MORPHISM_PRINT( );
# =#