Vector Spaces

class sage.categories.vector_spaces.VectorSpaces(K)

Bases: sage.categories.category_types.Category_module

The category of (abstract) vector spaces over a given field

??? with an embedding in an ambient vector space ???

EXAMPLES:

sage: VectorSpaces(QQ)
Category of vector spaces over Rational Field
sage: VectorSpaces(QQ).super_categories()
[Category of modules over Rational Field]

class DualObjects(category, *args)

Bases: sage.categories.dual.DualObjectsCategory

extra_super_categories()

Returns the dual category

EXAMPLES:

The category of algebras over the Rational Field is dual to the category of coalgebras over the same field:

sage: C = VectorSpaces(QQ)
sage: C.dual()
Category of duals of vector spaces over Rational Field
sage: C.dual().super_categories() # indirect doctest
[Category of vector spaces over Rational Field]

class VectorSpaces.ElementMethods

class VectorSpaces.ParentMethods

VectorSpaces.base_field()

Returns the base field over which the vector spaces of this category are all defined.

EXAMPLES:

sage: VectorSpaces(QQ).base_field()
Rational Field

VectorSpaces.super_categories(*args, **kwds)

EXAMPLES:

sage: VectorSpaces(QQ).super_categories()
[Category of modules over Rational Field]