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# Bimodules

class `sage.categories.bimodules.``Bimodules`(left_base, right_base, name=None)

  Bases: `sage.categories.category.CategoryWithParameters`

  The category of \((R,S)\)-bimodules

  For \(R\) and \(S\) rings, a \((R,S)\)-bimodule \(X\) is a left \(R\)-module and right \(S\)-module such that the left and right actions commute: \(r*(x*s) = (r*x)*s\).

  EXAMPLES:

      sage: Bimodules(QQ, ZZ)
      Category of bimodules over Rational Field on the left and Integer Ring on the right
      sage: Bimodules(QQ, ZZ).super_categories()
      [Category of left modules over Rational Field, Category of right modules over Integer Ring]

  class `ElementMethods`
  class `Bimodules.``ParentMethods`
  `Bimodules.``additional_structure`()

    Return `None`.

    Indeed, the category of bimodules defines no additional structure: a left and right module morphism between two bimodules is a bimodule morphism.

    See also

    `Category.additional_structure()`

    Todo

    Should this category be a `CategoryWithAxiom`?

    EXAMPLES:

        sage: Bimodules(QQ, ZZ).additional_structure()

  classmethod `Bimodules.``an_instance`()

    Return an instance of this class.

    EXAMPLES:

        sage: Bimodules.an_instance()
        Category of bimodules over Rational Field on the left and Real Field with 53 bits of precision on the right

  `Bimodules.``left_base_ring`()

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

    EXAMPLES:

        sage: Bimodules(QQ, ZZ).left_base_ring()
        Rational Field

  `Bimodules.``right_base_ring`()

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

    EXAMPLES:

        sage: Bimodules(QQ, ZZ).right_base_ring()
        Integer Ring

  `Bimodules.``super_categories`()

    EXAMPLES:

        sage: Bimodules(QQ, ZZ).super_categories()
        [Category of left modules over Rational Field, Category of right modules over Integer Ring]

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