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