Partially ordered monoids

class sage.categories.partially_ordered_monoids.PartiallyOrderedMonoids

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: $x\le y$ implies $x\ast z<y\ast z$ and $z\ast x<z\ast y$.

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]

Sage Live

PartiallyOrderedMonoids()
PartiallyOrderedMonoids().super_categories()

class ElementMethods

Bases: object

class ParentMethods

Bases: object

super_categories()

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]

Sage Live

PartiallyOrderedMonoids().super_categories()

Make live