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
¶ Bases:
object

class
ParentMethods
¶ Bases:
object

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

class