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).
Bases: sage.categories.category.Category
Initializes this category.
EXAMPLES:
sage: class SemiprimitiveRings(Category):
....: def super_categories(self):
....: return [Rings()]
....:
....: class ParentMethods:
....: def jacobson_radical(self):
....: return self.ideal(0)
....:
sage: C = SemiprimitiveRings()
sage: C
Category of semiprimitive rings
sage: C.__class__
<class '__main__.SemiprimitiveRings_with_category'>
Note
Specifying the name of this category by passing a string is deprecated. If the default name (built from the name of the class) is not adequate, please use _repr_object_names() to customize it.
x.__init__(...) initializes x; see help(type(x)) for signature
Bases: sage.categories.category_types.Category_in_ambient
Returns an instance of this class
EXAMPLES:
sage: AlgebraIdeals.an_instance()
Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field
x.__init__(...) initializes x; see help(type(x)) for signature
Bases: sage.categories.category.Category
Return the ambient object in which objects of this category are embedded.
Bases: sage.categories.category_types.AbelianCategory, sage.categories.category_types.Category_over_base_ring
Initialize self.
EXAMPLES:
sage: C = Algebras(GF(2)); C
Category of algebras over Finite Field of size 2
sage: TestSuite(C).run()
Bases: sage.categories.category.CategoryWithParameters
A base class for categories over some base object
INPUT:
Assumption: the classes for the parents, elements, morphisms, of
self should only depend on . See trac ticket #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
Returns an instance of this class
EXAMPLES:
sage: Algebras.an_instance()
Category of algebras over Rational Field
Return the base over which elements of this category are defined.
Bases: sage.categories.category_types.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()
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
Bases: sage.categories.category_types.Category_module
The category of all chain complexes over a base ring.
EXAMPLES:
sage: ChainComplexes(RationalField())
Category of chain complexes over Rational Field
sage: ChainComplexes(Integers(9))
Category of chain complexes over Ring of integers modulo 9
TESTS::
sage: TestSuite(ChainComplexes(RationalField())).run()
EXAMPLES:
sage: ChainComplexes(Integers(9)).super_categories()
[Category of modules with basis over Ring of integers modulo 9]
Bases: sage.categories.category.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
Returns an instance of this class
EXAMPLES:
sage: Elements(ZZ)
Category of elements of Integer Ring
x.__init__(...) initializes x; see help(type(x)) for signature
EXAMPLES:
sage: Elements(ZZ).super_categories()
[Category of objects]
TODO:
check that this is what we want.
Bases: sage.categories.category.Category
The category of sequences of elements of a given object.
This category is deprecated.
EXAMPLES:
sage: v = Sequence([1,2,3]); v
[1, 2, 3]
sage: C = v.category(); C
Category of sequences in Integer Ring
sage: loads(C.dumps()) == C
True
sage: Sequences(ZZ) is C
True
True
sage: Sequences(ZZ).category()
Category of objects
Returns an instance of this class
EXAMPLES:
sage: Elements(ZZ)
Category of elements of Integer Ring
x.__init__(...) initializes x; see help(type(x)) for signature
EXAMPLES:
sage: Sequences(ZZ).super_categories()
[Category of objects]
Bases: sage.categories.category.Category
The category of simplicial complexes.
EXAMPLES:
sage: SimplicialComplexes()
Category of simplicial complexes
TESTS:
sage: TestSuite(SimplicialComplexes()).run()
EXAMPLES:
sage: SimplicialComplexes().super_categories()
[Category of objects]