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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 $z*x < z*y$.

See Wikipedia article Ordered_monoid

EXAMPLES:

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

class ElementMethods

class ParentMethods

super_categories()

EXAMPLES:

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