Semigroups

sage.categories.semigroups.Semigroups

The category of (multiplicative) semigroups.

A semigroup is an associative magma, that is a set endowed with a multiplicative binary operation \(*\) which is associative (see Wikipedia article Semigroup).

The operation \(*\) is not required to have a neutral element. A semigroup for which such an element exists is a monoid.

EXAMPLES:

sage: C = Semigroups(); C
Category of semigroups
sage: C.super_categories()
[Category of magmas]
sage: C.all_super_categories()
[Category of semigroups, Category of magmas,
 Category of sets, Category of sets with partial maps, Category of objects]
sage: C.axioms()
frozenset({'Associative'})
sage: C.example()
An example of a semigroup: the left zero semigroup