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()

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