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()