Commutative additive groups

class sage.categories.commutative_additive_groups.CommutativeAdditiveGroups(base_category)

Bases: sage.categories.category_with_axiom.CategoryWithAxiom_singleton, sage.categories.category_types.AbelianCategory

The category of abelian groups, i.e. additive abelian monoids where each element has an inverse.

EXAMPLES:

sage: C = CommutativeAdditiveGroups(); C
Category of commutative additive groups
sage: C.super_categories()
[Category of additive groups, Category of commutative additive monoids]
sage: sorted(C.axioms())
['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveInverse', 'AdditiveUnital']
sage: C is CommutativeAdditiveMonoids().AdditiveInverse()
True
sage: from sage.categories.additive_groups import AdditiveGroups
sage: C is AdditiveGroups().AdditiveCommutative()
True

Note

This category is currently empty. It’s left there for backward compatibility and because it is likely to grow in the future.

class Algebras(category, *args)

Bases: sage.categories.algebra_functor.AlgebrasCategory

class CartesianProducts(category, *args)

Bases: sage.categories.cartesian_product.CartesianProductsCategory