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# Commutative algebras

class `sage.categories.commutative_algebras.``CommutativeAlgebras`(base_category)

  Bases: `sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring`

  The category of commutative algebras with unit over a given base ring.

  EXAMPLES:

      sage: M = CommutativeAlgebras(GF(19))
      sage: M
      Category of commutative algebras over Finite Field of size 19
      sage: CommutativeAlgebras(QQ).super_categories()
      [Category of algebras over Rational Field, Category of commutative rings]

  This is just a shortcut for:

      sage: Algebras(QQ).Commutative()
      Category of commutative algebras over Rational Field

  TESTS:

      sage: Algebras(QQ).Commutative() is CommutativeAlgebras(QQ)
      True
      sage: TestSuite(CommutativeAlgebras(ZZ)).run()

  Todo:

  > - product ( = cartesian product)
  > - coproduct ( = tensor product over base ring)

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