Additive Magmas

sage.categories.additive_magmas.AdditiveMagmas

The category of additive magmas.

An additive magma is a set endowed with a binary operation \(+\).

EXAMPLES:

sage: AdditiveMagmas()
Category of additive magmas
sage: AdditiveMagmas().super_categories()
[Category of sets]
sage: AdditiveMagmas().all_super_categories()
[Category of additive magmas, Category of sets, Category of sets with partial maps, Category of objects]

The following axioms are defined by this category:

sage: AdditiveMagmas().AdditiveAssociative()
Category of additive semigroups
sage: AdditiveMagmas().AdditiveUnital()
Category of additive unital additive magmas
sage: AdditiveMagmas().AdditiveCommutative()
Category of additive commutative additive magmas
sage: AdditiveMagmas().AdditiveUnital().AdditiveInverse()
Category of additive inverse additive unital additive magmas
sage: AdditiveMagmas().AdditiveAssociative().AdditiveCommutative()
Category of commutative additive semigroups
sage: AdditiveMagmas().AdditiveAssociative().AdditiveCommutative().AdditiveUnital()
Category of commutative additive monoids
sage: AdditiveMagmas().AdditiveAssociative().AdditiveCommutative().AdditiveUnital().AdditiveInverse()
Category of commutative additive groups