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]