Coverage for local/lib/python2.7/site-packages/sage/categories/objects.py : 28%

r""" 

Objects 

""" 

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

# Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> 

# William Stein <wstein@math.ucsd.edu> 

# 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr> 

# 2008-2013 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.misc.cachefunc import cached_method 

from sage.misc.superseded import deprecated_function_alias 

from sage.categories.category_singleton import Category_singleton 

from sage.categories.homsets import HomsetsCategory 

############################################################# 

# Generic category (default when requesting category of 

# an object using misc.functional.category 

############################################################# 

class Objects(Category_singleton): 

""" 

The category of all objects 

the basic category 

EXAMPLES:: 

sage: Objects() 

Category of objects 

sage: Objects().super_categories() 

[] 

TESTS:: 

sage: TestSuite(Objects()).run() 

""" 

def additional_structure(self): 

""" 

Return ``None`` 

Indeed, by convention, the category of objects defines no 

additional structure. 

.. SEEALSO:: :meth:`Category.additional_structure` 

EXAMPLES:: 

sage: Objects().additional_structure() 

""" 

return None 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: Objects().super_categories() 

[] 

""" 

return [] 

def __contains__(self, x): 

""" 

Anything is in the category of objects. 

EXAMPLES:: 

sage: int(1) in Objects() 

True 

sage: ZZ in Objects() 

True 

sage: 2/3 in Objects() 

True 

""" 

return True 

class SubcategoryMethods: 

@cached_method 

def Homsets(self): 

r""" 

Return the category of homsets between objects of this category. 

EXAMPLES:: 

sage: Sets().Homsets() 

Category of homsets of sets 

sage: Rings().Homsets() 

Category of homsets of unital magmas and additive unital additive magmas 

This used to be called ``hom_category``:: 

sage: Sets().hom_category() 

doctest:...: DeprecationWarning: hom_category is deprecated. Please use Homsets instead. 

See http://trac.sagemath.org/10668 for details. 

Category of homsets of sets 

.. NOTE:: Background 

Information, code, documentation, and tests about the 

category of homsets of a category ``Cs`` should go in 

the nested class ``Cs.Homsets``. They will then be 

made available to homsets of any subcategory of 

``Cs``. 

Assume, for example, that homsets of ``Cs`` are ``Cs`` 

themselves. This information can be implemented in the 

method ``Cs.Homsets.extra_super_categories`` to make 

``Cs.Homsets()`` a subcategory of ``Cs()``. 

Methods about the homsets themselves should go in the 

nested class ``Cs.Homsets.ParentMethods``. 

Methods about the morphisms can go in the nested class 

``Cs.Homsets.ElementMethods``. However it's generally 

preferable to put them in the nested class 

``Cs.MorphimMethods``; indeed they will then apply to 

morphisms of all subcategories of ``Cs``, and not only 

full subcategories. 

.. SEEALSO:: 

:class:`~.covariant_functorial_construction.FunctorialConstruction` 

.. TODO:: 

- Design a mechanism to specify that an axiom is 

compatible with taking subsets. Examples: 

``Finite``, ``Associative``, ``Commutative`` (when 

meaningful), but not ``Infinite`` nor ``Unital``. 

- Design a mechanism to specify that, when `B` is a 

subcategory of `A`, a `B`-homset is a subset of the 

corresponding `A` homset. And use it to recover all 

the relevant axioms from homsets in super categories. 

- For instances of redundant code due to this missing 

feature, see: 

- :meth:`AdditiveMonoids.Homsets.extra_super_categories` 

- :meth:`HomsetsCategory.extra_super_categories` 

(slightly different nature) 

- plus plenty of spots where this is not implemented. 

""" 

return HomsetsCategory.category_of(self) 

hom_category = deprecated_function_alias(10668, Homsets) 

@cached_method 

def Endsets(self): 

r""" 

Return the category of endsets between objects of this category. 

EXAMPLES:: 

sage: Sets().Endsets() 

Category of endsets of sets 

sage: Rings().Endsets() 

Category of endsets of unital magmas and additive unital additive magmas 

.. SEEALSO:: 

- :meth:`Homsets` 

""" 

return self.Homsets()._with_axiom("Endset") 

class ParentMethods: 

""" 

Methods for all category objects 

"""