### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »

# Commutative additive semigroups

class `sage.categories.commutative_additive_semigroups.``CommutativeAdditiveSemigroups`(base_category)

  Bases: `sage.categories.category_with_axiom.CategoryWithAxiom_singleton`

  The category of additive abelian semigroups, i.e. sets with an associative and abelian operation +.

  EXAMPLES:

      sage: C = CommutativeAdditiveSemigroups(); C
      Category of commutative additive semigroups
      sage: C.example()
      An example of a commutative monoid: the free commutative monoid generated by ('a', 'b', 'c', 'd')

      sage: sorted(C.super_categories(), key=str)
      [Category of additive commutative additive magmas,
       Category of additive semigroups]
      sage: sorted(C.axioms())
      ['AdditiveAssociative', 'AdditiveCommutative']
      sage: C is AdditiveMagmas().AdditiveAssociative().AdditiveCommutative()
      True

  Note

  This category is currently empty and only serves as a place holder to make `C.example()` work.

  TESTS:

      sage: TestSuite(C).run()

### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »