Bases: sage.categories.category_singleton.Category_singleton
The category of all objects the basic category
EXAMPLES:
sage: Objects()
Category of objects
sage: Objects().super_categories()
[]
TESTS:
sage: TestSuite(Objects()).run()
Methods for all category objects
Return the category of endsets between objects of this category.
EXAMPLES:
sage: Sets().Endsets()
Category of endsets of sets
sage: Rings().Endsets()
Category of endsets of unital magmas and additive unital additive magmas
See also
Return the category of homsets between objects of this category.
EXAMPLES:
sage: Sets().Homsets()
Category of homsets of sets
sage: Rings().Homsets()
Category of homsets of unital magmas and additive unital additive magmas
This used to be called hom_category:
sage: Sets().hom_category()
doctest:...: DeprecationWarning: hom_category is deprecated. Please use Homsets instead.
See http://trac.sagemath.org/10668 for details.
Category of homsets of sets
Note
Background
Information, code, documentation, and tests about the category of homsets of a category Cs should go in the nested class Cs.Homsets. They will then be made available to homsets of any subcategory of Cs.
Assume, for example, that homsets of Cs are Cs themselves. This information can be implemented in the method Cs.Homsets.extra_super_categories to make Cs.Homsets() a subcategory of Cs().
Methods about the homsets themselves should go in the nested class Cs.Homsets.ParentMethods.
Methods about the morphisms can go in the nested class Cs.Homsets.ElementMethods. However it’s generally preferable to put them in the nested class Cs.MorphimMethods; indeed they will then apply to morphisms of all subcategories of Cs, and not only full subcategories.
See also
FunctorialConstruction
Todo
Deprecated: Use Homsets() instead. See trac ticket #10668 for details.
Return None
Indeed, by convention, the category of objects defines no additional structure.
See also
EXAMPLES:
sage: Objects().additional_structure()
EXAMPLES:
sage: Objects().super_categories()
[]