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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] 

""" 

return [Posets(), Monoids()] 

 

class ParentMethods: 

pass 

 

class ElementMethods: 

pass