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.AbelianCategory#
Bases:
Category
- is_abelian()#
Return
True
asself
is an abelian category.EXAMPLES:
sage: CommutativeAdditiveGroups().is_abelian() True
- class sage.categories.category_types.Category_ideal(ambient, name=None)#
Bases:
Category_in_ambient
- classmethod an_instance()#
Return an instance of this class.
EXAMPLES:
sage: AlgebraIdeals.an_instance() Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field
- ring()#
Return the ambient ring used to describe objects
self
.EXAMPLES:
sage: C = Ideals(IntegerRing()) sage: C.ring() Integer Ring
- class sage.categories.category_types.Category_in_ambient(ambient, name=None)#
Bases:
Category
Initialize
self
.The parameter
name
is ignored.EXAMPLES:
sage: C = Ideals(IntegerRing()) sage: TestSuite(C).run()
- ambient()#
Return the ambient object in which objects of this category are embedded.
EXAMPLES:
sage: C = Ideals(IntegerRing()) sage: C.ambient() Integer Ring
- class sage.categories.category_types.Category_module(base, name=None)#
- class sage.categories.category_types.Category_over_base(base, name=None)#
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
self
should only depend on \(C\). See github 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
- classmethod an_instance()#
Returns an instance of this class
EXAMPLES:
sage: Algebras.an_instance() Category of algebras over Rational Field
- base()#
Return the base over which elements of this category are defined.
EXAMPLES:
sage: C = Algebras(QQ) sage: C.base() Rational Field
- class sage.categories.category_types.Category_over_base_ring(base, name=None)#
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()
- base_ring()#
Return the base ring over which elements of this category are defined.
EXAMPLES:
sage: C = Algebras(GF(2)) sage: C.base_ring() Finite Field of size 2
- class sage.categories.category_types.Elements(object)#
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
- classmethod an_instance()#
Returns an instance of this class
EXAMPLES:
sage: Elements.an_instance() Category of elements of Rational Field
- object()#
EXAMPLES:
sage: Elements(ZZ).object() Integer Ring
- super_categories()#
EXAMPLES:
sage: Elements(ZZ).super_categories() [Category of objects]
Todo
Check that this is what we want.