Commutative additive monoids#

class sage.categories.commutative_additive_monoids.CommutativeAdditiveMonoids(base_category)[source]#

Bases: CategoryWithAxiom_singleton

The category of commutative additive monoids, that is abelian additive semigroups with a unit

EXAMPLES:

Sage

sage: C = CommutativeAdditiveMonoids(); C
Category of commutative additive monoids
sage: C.super_categories()
[Category of additive monoids, Category of commutative additive semigroups]
sage: sorted(C.axioms())
['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveUnital']
sage: C is AdditiveMagmas().AdditiveAssociative().AdditiveCommutative().AdditiveUnital()
True

Python

>>> from sage.all import *
>>> C = CommutativeAdditiveMonoids(); C
Category of commutative additive monoids
>>> C.super_categories()
[Category of additive monoids, Category of commutative additive semigroups]
>>> sorted(C.axioms())
['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveUnital']
>>> C is AdditiveMagmas().AdditiveAssociative().AdditiveCommutative().AdditiveUnital()
True

Note

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