Additive semigroups

sage.categories.additive_semigroups.AdditiveSemigroups

The category of additive semigroups.

An additive semigroup is an associative additive magma, that is a set endowed with an operation \(+\) which is associative.

EXAMPLES:

sage: from sage.categories.additive_semigroups import AdditiveSemigroups
sage: C = AdditiveSemigroups(); C
Category of additive semigroups
sage: C.super_categories()
[Category of additive magmas]
sage: C.all_super_categories()
[Category of additive semigroups,
 Category of additive magmas,
 Category of sets,
 Category of sets with partial maps,
 Category of objects]

sage: C.axioms()
frozenset({'AdditiveAssociative'})
sage: C is AdditiveMagmas().AdditiveAssociative()
True