Coverage for local/lib/python2.7/site-packages/sage/categories/bialgebras.py : 23%

r""" 

Bialgebras 

""" 

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

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

# Copyright (C) 2008-2009 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_types import Category_over_base_ring 

from sage.categories.all import Algebras, Coalgebras 

from sage.categories.super_modules import SuperModulesCategory 

from sage.misc.lazy_import import LazyImport 

class Bialgebras(Category_over_base_ring): 

""" 

The category of bialgebras 

EXAMPLES:: 

sage: Bialgebras(ZZ) 

Category of bialgebras over Integer Ring 

sage: Bialgebras(ZZ).super_categories() 

[Category of algebras over Integer Ring, Category of coalgebras over Integer Ring] 

TESTS:: 

sage: TestSuite(Bialgebras(ZZ)).run() 

""" 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: Bialgebras(QQ).super_categories() 

[Category of algebras over Rational Field, Category of coalgebras over Rational Field] 

""" 

R = self.base_ring() 

return [Algebras(R), Coalgebras(R)] 

def additional_structure(self): 

r""" 

Return ``None``. 

Indeed, the category of bialgebras defines no additional 

structure: a morphism of coalgebras and of algebras between 

two bialgebras is a bialgebra morphism. 

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

.. TODO:: This category should be a :class:`CategoryWithAxiom`. 

EXAMPLES:: 

sage: Bialgebras(QQ).additional_structure() 

""" 

return None 

class Super(SuperModulesCategory): 

pass 

WithBasis = LazyImport('sage.categories.bialgebras_with_basis', 'BialgebrasWithBasis')