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