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r""" Partially ordered monoids """ #***************************************************************************** # Copyright (C) 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
from sage.categories.category_singleton import Category_singleton from sage.categories.basic import Posets, Monoids
class PartiallyOrderedMonoids(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:`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() """
def super_categories(self): """ EXAMPLES::
sage: PartiallyOrderedMonoids().super_categories() [Category of posets, Category of monoids] """
class ParentMethods: pass
class ElementMethods: pass |