Additive groups¶
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class
sage.categories.additive_groups.
AdditiveGroups
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
The category of additive groups.
An additive group is a set with an internal binary operation \(+\) which is associative, admits a zero, and where every element can be negated.
EXAMPLES:
sage: from sage.categories.additive_groups import AdditiveGroups sage: from sage.categories.additive_monoids import AdditiveMonoids sage: AdditiveGroups() Category of additive groups sage: AdditiveGroups().super_categories() [Category of additive inverse additive unital additive magmas, Category of additive monoids] sage: AdditiveGroups().all_super_categories() [Category of additive groups, Category of additive inverse additive unital additive magmas, Category of additive monoids, Category of additive unital additive magmas, Category of additive semigroups, Category of additive magmas, Category of sets, Category of sets with partial maps, Category of objects] sage: AdditiveGroups().axioms() frozenset({'AdditiveAssociative', 'AdditiveInverse', 'AdditiveUnital'}) sage: AdditiveGroups() is AdditiveMonoids().AdditiveInverse() True
TESTS:
sage: C = AdditiveGroups() sage: TestSuite(C).run()
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AdditiveCommutative
¶ alias of
CommutativeAdditiveGroups
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