Commutative additive semigroups¶
- class sage.categories.commutative_additive_semigroups.CommutativeAdditiveSemigroups(base_category)[source]¶
- Bases: - 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 - >>> 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.