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(s=None)

Bases: sage.categories.category.Category

is_abelian()

class sage.categories.category_types.Category_ideal(ambient, name=None)

Bases: sage.categories.category_types.Category_in_ambient

classmethod an_instance()

Returns an instance of this class

EXAMPLES:

sage: AlgebraIdeals.an_instance()
Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field

ring()

class sage.categories.category_types.Category_in_ambient(ambient, name=None)

Bases: sage.categories.category.Category

ambient()

Return the ambient object in which objects of this category are embedded.

class sage.categories.category_types.Category_module(base, name=None)

Bases: sage.categories.category_types.AbelianCategory, sage.categories.category_types.Category_over_base_ring

class sage.categories.category_types.Category_over_base(base, name=None)

Bases: sage.categories.category.Category

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.

class sage.categories.category_types.Category_over_base_ring(base, name=None)

Bases: sage.categories.category_types.Category_over_base

base_ring()

Return the base ring over which elements of this category are defined.

class sage.categories.category_types.ChainComplexes(base, name=None)

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()

super_categories(*args, **kwds)

EXAMPLES:

sage: ChainComplexes(Integers(9)).super_categories()
[Category of objects]

class sage.categories.category_types.Elements(object)

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

classmethod an_instance()

Returns an instance of this class

EXAMPLES:

sage: Elements(ZZ)
Category of elements of Integer Ring

object()

super_categories(*args, **kwds)

EXAMPLES:

  sage: Elements(ZZ).super_categories()
  [Category of objects]

TODO: check that this is what we want:

class sage.categories.category_types.Sequences(object)

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

classmethod an_instance()

Returns an instance of this class

EXAMPLES:

sage: Elements(ZZ)
Category of elements of Integer Ring

object()

super_categories(*args, **kwds)

EXAMPLES:

sage: Sequences(ZZ).super_categories()
[Category of objects]

class sage.categories.category_types.SimplicialComplexes(s=None)

Bases: sage.categories.category.Category

The category of simplicial complexes.

EXAMPLES:

sage: SimplicialComplexes()
Category of simplicial complexes

TESTS:

sage: TestSuite(SimplicialComplexes()).run()

super_categories(*args, **kwds)

EXAMPLES:

sage: SimplicialComplexes().super_categories()
[Category of objects]