Bases: sage.categories.category.Category
The category of (multiplicative) monoids, i.e. semigroups with a unit.
EXAMPLES:
sage: Monoids()
Category of monoids
sage: Monoids().super_categories()
[Category of semigroups]
sage: Monoids().all_super_categories()
[Category of monoids,
Category of semigroups,
Category of magmas,
Category of sets,
Category of sets with partial maps,
Category of objects]
TESTS:
sage: C = Monoids()
sage: TestSuite(C).run()
Returns whether self is the one of the monoid
The default implementation, is to compare with self.one().
TESTS:
sage: S = Monoids().example()
sage: S.one().is_one()
True
sage: S("aa").is_one()
False
Returns the one of the monoid, that is the unique neutral element for .
EXAMPLES:
sage: M = Monoids().example(); M
An example of a monoid: the free monoid generated by ('a', 'b', 'c', 'd')
sage: M.one()
''
Backward compatibility alias for self.one().
TESTS:
sage: S = Monoids().example()
sage: S.one_element()
''
n-ary product
Returns the product of the elements in , as an element of
.
EXAMPLES:
sage: S = Monoids().example() sage: S.prod([S(‘a’), S(‘b’)]) ‘ab’
Returns a list of the immediate super categories of self.
EXAMPLES:
sage: Monoids().super_categories()
[Category of semigroups]