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# 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 \(z*x < z*y\).

  http://en.wikipedia.org/wiki/Ordered_monoid

  EXAMPLES:

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

  TESTS:

      sage: TestSuite(PartiallyOrderedMonoids()).run()

  class `ElementMethods`
  class `PartiallyOrderedMonoids.``ParentMethods`
  `PartiallyOrderedMonoids.``super_categories`()

    EXAMPLES:

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

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