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# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Declarations
#
#! @Chapter Morphisms
#! Any GAP object satisfying <C>IsCapCategoryMorphism</C> can be added to a category
#! and then becomes a morphism in this category.
#! Any morphism can belong to one or no category.
#! After a GAP object is added to the category, it knows which things can be
#! computed in its category and to which category it belongs.
#! It knows categorical properties and attributes, and the functions for existential quantifiers
#! can be applied to the morphism.
###################################
##
#! @Section Attributes for the Type of Morphisms
##
###################################
#! @Description
#! The argument is a morphism $\alpha$.
#! The output is the category $\mathbf{C}$
#! to which $\alpha$ was added.
#! @Returns a category
#! @Arguments alpha
DeclareAttribute( "CapCategory",
IsCapCategoryMorphism );
#! @Description
#! The argument is a morphism $\alpha: a \rightarrow b$.
#! The output is its source $a$.
#! @Returns an object
#! @Arguments alpha
DeclareAttribute( "Source",
IsCapCategoryMorphism );
#! @Description
#! The argument is a morphism $\alpha: a \rightarrow b$.
#! The output is its range $b$.
#! @Returns an object
#! @Arguments alpha
DeclareAttribute( "Range",
IsCapCategoryMorphism );
#! @Description
#! The argument is a morphism $\alpha: a \rightarrow b$.
#! The output is its target $b$.
#! @Returns an object
#! @Arguments alpha
DeclareAttribute( "Target",
IsCapCategoryMorphism );
###################################
##
#! @Section Technical stuff
##
###################################
DeclareGlobalFunction( "CAP_INTERNAL_CREATE_MORPHISM_PRINT" );
DeclareGlobalFunction( "INSTALL_TODO_LIST_FOR_EQUAL_MORPHISMS" );
DeclareGlobalVariable( "PROPAGATION_LIST_FOR_EQUAL_MORPHISMS" );
## adds the given string to PROPAGATION_LIST_FOR_EQUAL_MORPHISMS
DeclareOperation( "AddPropertyToMatchAtIsCongruentForMorphisms",
[ IsCapCategory, IsString ] );
###################################
##
#! @Section Adding Morphisms to a Category
#! @SectionLabel Adding_Morphisms_to_a_Category
##
###################################
#! @Description
#! Adds <A>morphism</A> as a morphism to <A>category</A>.
#! @Arguments category, morphism
DeclareOperation( "Add",
[ IsCapCategory, IsCapCategoryMorphism ] );
#! @Description
#! Adds <A>morphism</A> as a morphism to <A>category</A>.
#! If <A>morphism</A> already lies in the filter <C>IsCapCategoryMorphism</C>,
#! the operation <Ref Oper="Add" Label="for IsCapCategory, IsCapCategoryMorphism" />
#! can be used instead.
#! @Arguments category, morphism
DeclareOperation( "AddMorphism",
[ IsCapCategory, IsAttributeStoringRep ] );
#! @Arguments category, source, range[, attr1, val1, attr2, val2, ...]
#! @Description
#! Creates a morphism in <A>category</A> with the given attributes.
#! @Returns a morphism
DeclareGlobalFunction( "CreateCapCategoryMorphismWithAttributes" );
#! @Arguments category, source, value, range
#! @Description
#! EXPERIMENTAL: This specification might change any time without prior notice.
#! Views <A>value</A> as a morphism from <A>source</A> to <A>range</A> in <A>category</A>.
#! @Returns a morphism
DeclareGlobalFunction( "AsCapCategoryMorphism" );
#! @BeginGroup
#! @Description
#! EXPERIMENTAL: This specification might change any time without prior notice.
#! Views a morphism obtained via <Ref Func="AsCapCategoryMorphism" /> as a primitive value again.
#! Here, the word **primitive** means **primitive from the perspective of the category**.
#! For example, from the perspective of an opposite category, morphisms of the underlying category
#! are primitive values.
#! The attribute is chosen according to the morphism datum type:
#! * For `IsInt`, the attribute `AsInteger` is used.
#! * For `IsHomalgMatrix`, the attribute `AsHomalgMatrix` is used.
#!
#! In all other cases or if no morphism datum type is given, the attribute `AsPrimitiveValue` is used.
#! @Returns a value
#! @Arguments morphism
DeclareAttribute( "AsPrimitiveValue", IsCapCategoryMorphism );
#! @Arguments morphism
DeclareAttribute( "AsInteger", IsCapCategoryMorphism );
#! @Arguments morphism
DeclareAttribute( "AsHomalgMatrix", IsCapCategoryMorphism );
#! @EndGroup
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