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# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Implementations
#
#############################################################################
##
## Chapter Product category
##
#############################################################################
# backwards compatibility
BindGlobal( "IsCapCategoryProductObjectRep", IsCapCategoryProductObject );
# backwards compatibility
BindGlobal( "IsCapCategoryProductMorphismRep", IsCapCategoryProductMorphism );
# backwards compatibility
BindGlobal( "IsCapCategoryProductTwoCellRep", IsCapCategoryProductTwoCell );
BindGlobal( "TheTypeOfCapCategoryProductObjects",
NewType( TheFamilyOfCapCategoryObjects,
IsCapCategoryProductObject ) );
BindGlobal( "TheTypeOfCapCategoryProductMorphisms",
NewType( TheFamilyOfCapCategoryMorphisms,
IsCapCategoryProductMorphism ) );
BindGlobal( "TheTypeOfCapCategoryProductTwoCells",
NewType( TheFamilyOfCapCategoryTwoCells,
IsCapCategoryProductTwoCell ) );
###################################
##
## Section Fallback methods for functors
##
###################################
##
InstallMethod( Components,
[ IsCapProductCategory ],
i -> [ i ] );
##
InstallMethod( Components,
[ IsCapCategoryProductObject ],
i -> [ i ] );
##
InstallMethod( Components,
[ IsCapCategoryProductMorphism ],
i -> [ i ] );
##
InstallMethod( Components,
[ IsCapCategoryProductTwoCell ],
i -> [ i ] );
###################################
##
## Section Constructor
##
###################################
BindGlobal( "CAP_INTERNAL_CREATE_PRODUCT_ARGUMENT_LIST",
function( arg_list )
local nr_components, current_argument, i, j, current_mat, new_args;
i := 1;
while IsInt( arg_list[ i ] ) do
i := i + 1;
od;
if IsCapCategoryCell( arg_list[ 1 ] ) or IsCapCategory( arg_list[ 1 ] ) then
nr_components := Length( arg_list[ 1 ] );
elif IsList( arg_list[ 1 ] ) then
nr_components := Length( arg_list[ 1 ][ 1 ] );
fi;
new_args := List( [ 1 .. nr_components ], i -> [ ] );
for i in [ 1 .. Length( arg_list ) ] do
current_argument := arg_list[ i ];
if IsCapCategoryCell( current_argument ) or IsCapCategory( current_argument ) then
for j in [ 1 .. nr_components ] do
new_args[ j ][ i ] := current_argument[ j ];
od;
elif IsInt( current_argument ) then
for j in [ 1 .. nr_components ] do
new_args[ j ][ i ] := current_argument;
od;
elif IsList( current_argument ) then
current_mat := TransposedMat( List( current_argument, Components ) );
for j in [ 1 .. nr_components ] do
new_args[ j ][ i ] := current_mat[ j ];
od;
else
Error( "Unrecognized argument type" );
fi;
od;
return new_args;
end );
##
BindGlobal( "CAP_INTERNAL_INSTALL_PRODUCT_ADDS_FROM_CATEGORY",
function( product_category )
local recnames, current_recname, current_entry, func,
current_add, create_func, components;
recnames := RecNames( CAP_INTERNAL_METHOD_NAME_RECORD );
components := Components( product_category );
for current_recname in recnames do
current_entry := CAP_INTERNAL_METHOD_NAME_RECORD.( current_recname );
if not ForAll( current_entry.filter_list, filter -> filter in [ "category", "object", "morphism", "twocell", "integer", "list_of_objects", "list_of_morphisms", "list_of_twocells" ] ) then
continue;
fi;
if not current_entry.return_type in [ "object", "morphism", "twocell", "bool" ] then
continue;
fi;
if ForAny( components, category -> not CanCompute( category, current_recname ) ) then
continue;
fi;
create_func := function( current_name )
if current_entry.return_type = "bool" then
return function( cat, arg... )
local product_args, result_list;
product_args := CAP_INTERNAL_CREATE_PRODUCT_ARGUMENT_LIST( arg );
result_list := List( product_args, i -> CallFuncList( ValueGlobal( current_name ), i ) );
return ForAll( result_list, IdFunc );
end;
elif current_entry.return_type = "object" then
return function( cat, arg... )
local product_args, result_list;
product_args := CAP_INTERNAL_CREATE_PRODUCT_ARGUMENT_LIST( arg );
result_list := List( product_args, i -> CallFuncList( ValueGlobal( current_name ), i ) );
return ProductCategoryObject( cat, result_list );
end;
elif current_entry.return_type = "morphism" then
return function( cat, arg... )
local product_args, result_list;
product_args := CAP_INTERNAL_CREATE_PRODUCT_ARGUMENT_LIST( arg );
result_list := List( product_args, i -> CallFuncList( ValueGlobal( current_name ), i ) );
return ProductCategoryMorphism( cat, result_list );
end;
elif current_entry.return_type = "twocell" then
return function( cat, arg... )
local product_args, result_list;
product_args := CAP_INTERNAL_CREATE_PRODUCT_ARGUMENT_LIST( arg );
result_list := List( product_args, i -> CallFuncList( ValueGlobal( current_name ), i ) );
return ProductCategoryTwoCell( cat, result_list );
end;
else
Error( "this should never happen" );
fi;
end;
func := create_func( current_recname );
current_add := ValueGlobal( Concatenation( "Add", current_recname ) );
current_add( product_category, func );
od;
end );
##
InstallMethodWithCrispCache( ProductCategory,
[ IsList ],
function( category_list )
local product_category, namestring;
if not ForAll( category_list, IsFinalized ) then
Error( "all categories for the product must be finalized" );
fi;
## this is the convention in CapCat
if Length( category_list ) = 1 then
return category_list[1];
fi;
namestring := JoinStringsWithSeparator( List( category_list, Name ), ", " );
namestring := Concatenation( "Product of: " , namestring );
product_category := CreateCapCategory( namestring, IsCapProductCategory, IsCapCategoryProductObject, IsCapCategoryProductMorphism, IsCapCategoryProductTwoCell );
SetComponents( product_category, category_list );
SetLength( product_category, Length( category_list ) );
CAP_INTERNAL_INSTALL_PRODUCT_ADDS_FROM_CATEGORY( product_category );
Finalize( product_category );
return product_category;
end );
##
InstallMethodWithCacheFromObject( ProductCategoryObject,
[ IsCapProductCategory, IsList ],
function( category, object_list )
return CreateCapCategoryObjectWithAttributes(
category,
Components, object_list,
Length, Length( object_list )
);
end : ArgumentNumber := 1 );
##
InstallMethodWithCacheFromObject( ProductCategoryMorphism,
[ IsCapProductCategory, IsList ],
function( category, morphism_list )
local source, range;
source := ProductCategoryObject( category, List( morphism_list, Source ) );
range := ProductCategoryObject( category, List( morphism_list, Range ) );
return CreateCapCategoryMorphismWithAttributes(
category,
source, range,
Components, morphism_list,
Length, Length( morphism_list )
);
end : ArgumentNumber := 1 );
##
InstallMethodWithCacheFromObject( ProductCategoryTwoCell,
[ IsCapProductCategory, IsList ],
function( category, twocell_list )
local source, range;
source := ProductCategoryMorphism( category, List( twocell_list, Source ) );
range := ProductCategoryMorphism( category, List( twocell_list, Range ) );
return CreateCapCategoryTwoCellWithAttributes(
category,
source, range,
Components, twocell_list,
Length, Length( twocell_list )
);
end : ArgumentNumber := 1 );
##
InstallOtherMethod( \/,
[ IsList, IsCapProductCategory ],
function( list, category )
if ForAll( list, IsCapCategoryObject ) then
return ProductCategoryObject( category, list );
elif ForAll( list, IsCapCategoryMorphism ) then
return ProductCategoryMorphism( category, list );
elif ForAll( list, IsCapCategoryTwoCell ) then
return ProductCategoryTwoCell( category, list );
else
Error( "Wrong input!\n" );
fi;
end );
##
InstallMethod( \[\],
[ IsCapProductCategory, IsInt ],
function( category, index )
if Length( category ) < index then
Error( "index too high, cannot compute this Component" );
fi;
return Components( category )[ index ];
end );
##
InstallMethod( \[\],
[ IsCapCategoryProductObject, IsInt ],
function( cell, index )
if Length( cell ) < index then
Error( "index too high, cannot compute this Component" );
fi;
return Components( cell )[ index ];
end );
##
InstallMethod( \[\],
[ IsCapCategoryProductMorphism, IsInt ],
function( cell, index )
if Length( cell ) < index then
Error( "index too high, cannot compute this Component" );
fi;
return Components( cell )[ index ];
end );
##
InstallMethod( \[\],
[ IsCapCategoryProductTwoCell, IsInt ],
function( cell, index )
if Length( cell ) < index then
Error( "index too high, cannot compute this Component" );
fi;
return Components( cell )[ index ];
end );
###################################
##
## Section Morphism function
##
###################################
##
InstallMethodWithCacheFromObject( HorizontalPreCompose,
[ IsCapCategoryProductTwoCell, IsCapCategoryProductTwoCell ],
function( twocell_left, twocell_right )
local left_comp, right_comp;
left_comp := Components( twocell_left );
right_comp := Components( twocell_right );
return ProductCategoryTwoCell( CapCategory( twocell_left ), List( [ 1 .. Length( twocell_left ) ], i -> HorizontalPreCompose( left_comp[ i ], right_comp[ i ] ) ) );
end );
##
InstallMethodWithCacheFromObject( VerticalPreCompose,
[ IsCapCategoryProductTwoCell, IsCapCategoryProductTwoCell ],
function( twocell_left, twocell_right )
local left_comp, right_comp;
left_comp := Components( twocell_left );
right_comp := Components( twocell_right );
return ProductCategoryTwoCell( CapCategory( twocell_left ), List( [ 1 .. Length( twocell_left ) ], i -> VerticalPreCompose( left_comp[ i ], right_comp[ i ] ) ) );
end );
###################################
##
## Functors on the product category
##
###################################
##
InstallMethodWithCache( DirectProductFunctor,
[ IsCapCategory, IsInt ],
function( category, number_of_arguments )
local direct_product_functor;
direct_product_functor := CapFunctor(
Concatenation( "direct_product_on_", Name( category ), "_for_", String( number_of_arguments ), "_arguments" ),
ProductCategory( List( [ 1 .. number_of_arguments ], c -> category ) ),
category
);
AddObjectFunction( direct_product_functor,
function( object )
return CallFuncList( DirectProduct, Components( object ) );
end );
AddMorphismFunction( direct_product_functor,
function( new_source, morphism_list, new_range )
local source, new_source_list;
new_source_list := List( morphism_list, Source );
source := List( [ 1 .. number_of_arguments ], i ->
PreCompose( ProjectionInFactorOfDirectProduct( new_source_list, i ), morphism_list[i] ) );
return CallFuncList( UniversalMorphismIntoDirectProduct, source );
end );
return direct_product_functor;
end );
##
InstallMethodWithCache( CoproductFunctor,
[ IsCapCategory, IsInt ],
function( category, number_of_arguments )
local coproduct_functor;
coproduct_functor := CapFunctor(
Concatenation( "coproduct_on_", Name( category ), "_for_", String( number_of_arguments ), "_arguments" ),
ProductCategory( List( [ 1 .. number_of_arguments ], c -> category ) ),
category
);
AddObjectFunction( coproduct_functor,
function( object )
return Coproduct( Components( object ) );
end );
AddMorphismFunction( coproduct_functor,
function( new_source, morphism_list, new_range )
local sink, new_range_list;
new_range_list := List( morphism_list, Range );
sink := List( [ 1 .. number_of_arguments ], i ->
PreCompose( morphism_list[i], InjectionOfCofactorOfCoproduct( new_range_list, i ) ) );
return CallFuncList( UniversalMorphismFromCoproduct, sink );
end );
return coproduct_functor;
end );
###################################
##
## Section Some hacks
##
###################################
#= comment for Julia
BindGlobal( "CAP_INTERNAL_PRODUCT_SAVE", Product );
MakeReadWriteGlobal( "Product" );
## HEHE!
Product := function( arg )
if not IsEmpty( arg ) then
if ForAll( arg, IsCapCategory ) then
return ProductCategory( arg );
elif ForAll( arg, IsCapCategoryCell ) then
return arg / ProductCategory( List( arg, CapCategory ) );
fi;
fi;
return CallFuncList( CAP_INTERNAL_PRODUCT_SAVE, arg );
end;
MakeReadOnlyGlobal( "Product" );
# =#
##
InstallMethod( IsEqualForCache,
[ IsCapProductCategory, IsCapProductCategory ],
function( category1, category2 )
local list1, list2, length;
list1 := Components( category1 );
list2 := Components( category2 );
length := Length( list1 );
if length <> Length( list2 ) then
return false;
fi;
return ForAll( [ 1 .. length ], i -> IsEqualForCache( list1[ i ], list2[ i ] ) );
end );
##
InstallMethod( IsEqualForCache,
[ IsCapCategoryProductObject, IsCapCategoryProductObject ],
function( obj1, obj2 )
local list1, list2, length;
list1 := Components( obj1 );
list2 := Components( obj2 );
length := Length( list1 );
if length <> Length( list2 ) then
return false;
fi;
return ForAll( [ 1 .. length ], i -> IsEqualForCache( list1[ i ], list2[ i ] ) );
end );
##
InstallMethod( IsEqualForCache,
[ IsCapCategoryProductMorphism, IsCapCategoryProductMorphism ],
function( obj1, obj2 )
local list1, list2, length;
list1 := Components( obj1 );
list2 := Components( obj2 );
length := Length( list1 );
if length <> Length( list2 ) then
return false;
fi;
return ForAll( [ 1 .. length ], i -> IsEqualForCache( list1[ i ], list2[ i ] ) );
end );
##
InstallMethod( IsEqualForCache,
[ IsCapCategoryProductTwoCell, IsCapCategoryProductTwoCell ],
function( obj1, obj2 )
local list1, list2, length;
list1 := Components( obj1 );
list2 := Components( obj2 );
length := Length( list1 );
if length <> Length( list2 ) then
return false;
fi;
return ForAll( [ 1 .. length ], i -> IsEqualForCache( list1[ i ], list2[ i ] ) );
end );
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