Finitely generated semigroups

sage.categories.finitely_generated_semigroups.FinitelyGeneratedSemigroups

The category of finitely generated (multiplicative) semigroups.

A finitely generated semigroup is a semigroup endowed with a distinguished finite set of generators (see FinitelyGeneratedSemigroups.ParentMethods.semigroup_generators()). This makes it into an enumerated set.

EXAMPLES:

sage: C = Semigroups().FinitelyGenerated(); C
Category of finitely generated semigroups
sage: C.super_categories()
[Category of semigroups,
 Category of finitely generated magmas,
 Category of enumerated sets]
sage: sorted(C.axioms())
['Associative', 'Enumerated', 'FinitelyGeneratedAsMagma']
sage: C.example()
An example of a semigroup: the free semigroup generated by ('a', 'b', 'c', 'd')