Partially ordered monoids#

class sage.categories.partially_ordered_monoids.PartiallyOrderedMonoids[source]#

Bases: 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

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

Python

>>> from sage.all import *
>>> PartiallyOrderedMonoids()
Category of partially ordered monoids
>>> PartiallyOrderedMonoids().super_categories()
[Category of posets, Category of monoids]

class ElementMethods[source]#: Bases: object

class ParentMethods[source]#: Bases: object

super_categories()[source]#

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> PartiallyOrderedMonoids().super_categories()
[Category of posets, Category of monoids]