Specific category classes¶
This is placed in a separate file from categories.py to avoid circular imports (as morphisms must be very low in the hierarchy with the new coercion model).
- class sage.categories.category_types.Category_ideal(ambient, name=None)[source]¶
- Bases: - Category_in_ambient- classmethod an_instance()[source]¶
- Return an instance of this class. - EXAMPLES: - sage: AlgebraIdeals.an_instance() Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field - >>> from sage.all import * >>> AlgebraIdeals.an_instance() Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field 
 
- class sage.categories.category_types.Category_in_ambient(ambient, name=None)[source]¶
- Bases: - Category- Initialize - self.- The parameter - nameis ignored.- EXAMPLES: - sage: C = Ideals(IntegerRing()) sage: TestSuite(C).run() - >>> from sage.all import * >>> C = Ideals(IntegerRing()) >>> TestSuite(C).run() 
- class sage.categories.category_types.Category_over_base(base, name=None)[source]¶
- Bases: - CategoryWithParameters- A base class for categories over some base object. - INPUT: - base– a category \(C\) or an object of such a category
 - Assumption: the classes for the parents, elements, morphisms, of - selfshould only depend on \(C\). See Issue #11935 for details.- EXAMPLES: - sage: Algebras(GF(2)).element_class is Algebras(GF(3)).element_class True sage: C = GF(2).category() sage: Algebras(GF(2)).parent_class is Algebras(C).parent_class True sage: C = ZZ.category() sage: Algebras(ZZ).element_class is Algebras(C).element_class True - >>> from sage.all import * >>> Algebras(GF(Integer(2))).element_class is Algebras(GF(Integer(3))).element_class True >>> C = GF(Integer(2)).category() >>> Algebras(GF(Integer(2))).parent_class is Algebras(C).parent_class True >>> C = ZZ.category() >>> Algebras(ZZ).element_class is Algebras(C).element_class True 
- class sage.categories.category_types.Category_over_base_ring(base, name=None)[source]¶
- Bases: - Category_over_base- Initialize - self.- EXAMPLES: - sage: C = Algebras(GF(2)); C Category of algebras over Finite Field of size 2 sage: TestSuite(C).run() - >>> from sage.all import * >>> C = Algebras(GF(Integer(2))); C Category of algebras over Finite Field of size 2 >>> TestSuite(C).run() 
- class sage.categories.category_types.Elements(object)[source]¶
- Bases: - Category- The category of all elements of a given parent. - EXAMPLES: - sage: a = IntegerRing()(5) sage: C = a.category(); C Category of elements of Integer Ring sage: a in C True sage: 2/3 in C False sage: loads(C.dumps()) == C True - >>> from sage.all import * >>> a = IntegerRing()(Integer(5)) >>> C = a.category(); C Category of elements of Integer Ring >>> a in C True >>> Integer(2)/Integer(3) in C False >>> loads(C.dumps()) == C True - classmethod an_instance()[source]¶
- Return an instance of this class. - EXAMPLES: - sage: Elements.an_instance() Category of elements of Rational Field - >>> from sage.all import * >>> Elements.an_instance() Category of elements of Rational Field