Commutative additive semigroups - Category Framework

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# Commutative additive semigroups

class sage.categories.commutative_additive_semigroups.CommutativeAdditiveSemigroups(base_category)

  Bases: `CategoryWithAxiom_singleton`

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

  EXAMPLES:

  Sage

      sage: C = CommutativeAdditiveSemigroups(); C
      Category of commutative additive semigroups
      sage: C.example()
      An example of a commutative semigroup: the free commutative semigroup 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

  Python

      >>> from sage.all import *
      >>> C = CommutativeAdditiveSemigroups(); C
      Category of commutative additive semigroups
      >>> C.example()
      An example of a commutative semigroup: the free commutative semigroup generated by ('a', 'b', 'c', 'd')

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

  Note

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