Partially ordered monoids¶
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sage.categories.partially_ordered_monoids.PartiallyOrderedMonoids(s=None)¶ Bases:
sage.categories.category_singleton.Category_singletonThe 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]
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ElementMethods¶ Bases:
object
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ParentMethods¶ Bases:
object
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super_categories()¶ EXAMPLES:
sage: PartiallyOrderedMonoids().super_categories() [Category of posets, Category of monoids]
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