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# Additive groups

class `sage.categories.additive_groups.``AdditiveGroups`(base_category)

  Bases: `sage.categories.category_with_axiom.CategoryWithAxiom_singleton`

  The category of additive groups.

  An additive group is a set with an internal binary operation \(+\) which is associative, admits a zero, and where every element can be negated.

  EXAMPLES:

      sage: from sage.categories.additive_groups import AdditiveGroups
      sage: from sage.categories.additive_monoids import AdditiveMonoids
      sage: AdditiveGroups()
      Category of additive groups
      sage: AdditiveGroups().super_categories()
      [Category of additive inverse additive unital additive magmas,
       Category of additive monoids]
      sage: AdditiveGroups().all_super_categories()
      [Category of additive groups,
       Category of additive inverse additive unital additive magmas,
       Category of additive monoids,
       Category of additive unital additive magmas,
       Category of additive semigroups,
       Category of additive magmas,
       Category of sets,
       Category of sets with partial maps,
       Category of objects]

      sage: AdditiveGroups().axioms()
      frozenset({'AdditiveAssociative', 'AdditiveInverse', 'AdditiveUnital'})
      sage: AdditiveGroups() is AdditiveMonoids().AdditiveInverse()
      True

  TESTS:

      sage: C = AdditiveGroups()
      sage: TestSuite(C).run()

  `AdditiveCommutative`

    alias of `CommutativeAdditiveGroups`

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