Algebra Functorial Construction

AUTHORS:

  • Nicolas M. Thiery (2010): initial revision
class sage.categories.algebra_functor.AlgebraFunctor(base_ring)

Bases: sage.categories.covariant_functorial_construction.CovariantFunctorialConstruction

A singleton class for the algebra functor.

base_ring()

Return the base ring for this functor.

EXAMPLES:

sage: from sage.categories.algebra_functor import AlgebraFunctor
sage: AlgebraFunctor(QQ).base_ring()
Rational Field
class sage.categories.algebra_functor.AlgebrasCategory(category, *args)

Bases: sage.categories.covariant_functorial_construction.CovariantConstructionCategory, sage.categories.category_types.Category_over_base_ring

An abstract base class for categories of monoid algebras, groups algebras, and the like.

See also

INPUT:

  • base_ring – a ring

EXAMPLES:

sage: C = Monoids().Algebras(QQ); C
Category of monoid algebras over Rational Field
sage: C = Groups().Algebras(QQ); C
Category of group algebras over Rational Field

sage: C._short_name()
'Algebras'
sage: latex(C) # todo: improve that
\mathbf{Algebras}(\mathbf{Groups})