Finitely generated semigroups¶
-
sage.categories.finitely_generated_semigroups.
FinitelyGeneratedSemigroups
¶ The category of finitely generated (multiplicative) semigroups.
A
finitely generated semigroup
is asemigroup
endowed with a distinguished finite set of generators (seeFinitelyGeneratedSemigroups.ParentMethods.semigroup_generators()
). This makes it into anenumerated 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')