# Partially ordered monoids¶

class sage.categories.partially_ordered_monoids.PartiallyOrderedMonoids(s=None)

Bases: sage.categories.category_singleton.Category_singleton

The category of partially ordered monoids, that is partially ordered sets which are also monoids, and such that multiplication preserves the ordering: $$x \leq y$$ implies $$x*z < y*z$$ and $$z*x < z*y$$.

http://en.wikipedia.org/wiki/Ordered_monoid

EXAMPLES:

sage: PartiallyOrderedMonoids()
Category of partially ordered monoids
sage: PartiallyOrderedMonoids().super_categories()
[Category of posets, Category of monoids]


TESTS:

sage: TestSuite(PartiallyOrderedMonoids()).run()

class ElementMethods
class PartiallyOrderedMonoids.ParentMethods
PartiallyOrderedMonoids.super_categories()

EXAMPLES:

sage: PartiallyOrderedMonoids().super_categories()
[Category of posets, Category of monoids]


Objects

Posets