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# 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

  - `Sets.ParentMethods.algebra()`
  - `Sets.SubcategoryMethods.Algebras()`
  - `CovariantFunctorialConstruction`

  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})

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