Coverage for local/lib/python2.7/site-packages/sage/categories/subobjects.py : 17%

""" 

Subobjects Functorial Construction 

AUTHORS: 

- Nicolas M. Thiery (2010): initial revision 

""" 

#***************************************************************************** 

# Copyright (C) 2009 Nicolas M. Thiery <nthiery at users.sf.net> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

from sage.categories.category import Category 

from sage.categories.covariant_functorial_construction import RegressiveCovariantConstructionCategory 

class SubobjectsCategory(RegressiveCovariantConstructionCategory): 

_functor_category = "Subobjects" 

@classmethod 

def default_super_categories(cls, category): 

""" 

Returns the default super categories of ``category.Subobjects()`` 

Mathematical meaning: if `A` is a subobject of `B` in the 

category `C`, then `A` is also a subquotient of `B` in the 

category `C`. 

INPUT: 

- ``cls`` -- the class ``SubobjectsCategory`` 

- ``category`` -- a category `Cat` 

OUTPUT: a (join) category 

In practice, this returns ``category.Subquotients()``, joined 

together with the result of the method 

:meth:`RegressiveCovariantConstructionCategory.default_super_categories() <sage.categories.covariant_functorial_construction.RegressiveCovariantConstructionCategory.default_super_categories>` 

(that is the join of ``category`` and ``cat.Subobjects()`` for 

each ``cat`` in the super categories of ``category``). 

EXAMPLES: 

Consider ``category=Groups()``, which has ``cat=Monoids()`` as 

super category. Then, a subgroup of a group `G` is 

simultaneously a subquotient of `G`, a group by itself, and a 

submonoid of `G`:: 

sage: Groups().Subobjects().super_categories() 

[Category of groups, Category of subquotients of monoids, Category of subobjects of sets] 

Mind the last item above: there is indeed currently nothing 

implemented about submonoids. 

This resulted from the following call:: 

sage: sage.categories.subobjects.SubobjectsCategory.default_super_categories(Groups()) 

Join of Category of groups and Category of subquotients of monoids and Category of subobjects of sets 

""" 

return Category.join([category.Subquotients(), super(SubobjectsCategory, cls).default_super_categories(category)])