Objects

class sage.categories.objects.Objects(s=None)

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()
class ElementMethods
class Objects.HomCategory(category, name=None)

Bases: sage.categories.category.HomCategory

Initializes this HomCategory

INPUT:
  • category – the category whose Homsets are the objects of this category.
  • name – An optional name for this category.

EXAMPLES:

We need to skip one test, since the hierarchy of hom categories isn’t consistent yet:

sage: C = sage.categories.category.HomCategory(Rings()); C
Category of hom sets in Category of rings
sage: TestSuite(C).run(skip=['_test_category_graph'])
class ParentMethods
Objects.HomCategory.extra_super_categories()

This declares that any homset \(Hom(A, B)\) for \(A\) and \(B\) in the category of objects is a set. This more or less assumes that the category is locally small. See http://en.wikipedia.org/wiki/Category_(mathematics)

EXAMPLES:

sage: Objects().hom_category().extra_super_categories()
[Category of sets]
class Objects.ParentMethods
Objects.super_categories()

EXAMPLES:

sage: Objects().super_categories()
[]

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