Magmas¶
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sage.categories.magmas.
Magmas
¶ The category of (multiplicative) magmas.
A magma is a set with a binary operation \(*\).
EXAMPLES:
sage: Magmas() Category of magmas sage: Magmas().super_categories() [Category of sets] sage: Magmas().all_super_categories() [Category of magmas, Category of sets, Category of sets with partial maps, Category of objects]
The following axioms are defined by this category:
sage: Magmas().Associative() Category of semigroups sage: Magmas().Unital() Category of unital magmas sage: Magmas().Commutative() Category of commutative magmas sage: Magmas().Unital().Inverse() Category of inverse unital magmas sage: Magmas().Associative() Category of semigroups sage: Magmas().Associative().Unital() Category of monoids sage: Magmas().Associative().Unital().Inverse() Category of groups