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r""" Groupoid """ from __future__ import absolute_import #***************************************************************************** # Copyright (C) 2008 David Kohel <kohel@maths.usyd.edu> and # William Stein <wstein@math.ucsd.edu> # 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 CategoryWithParameters from .sets_cat import Sets
class Groupoid(CategoryWithParameters): """ The category of groupoids, for a set (usually a group) `G`.
FIXME:
- Groupoid or Groupoids ? - definition and link with :wikipedia:`Groupoid` - Should Groupoid inherit from Category_over_base?
EXAMPLES::
sage: Groupoid(DihedralGroup(3)) Groupoid with underlying set Dihedral group of order 6 as a permutation group
"""
def __init__(self, G = None): """ TESTS::
sage: S8 = SymmetricGroup(8) sage: C = Groupoid(S8) sage: TestSuite(C).run() """ from sage.groups.perm_gps.permgroup_named import SymmetricGroup G = SymmetricGroup(8)
def _repr_(self): """ EXAMPLES::
sage: S8 = SymmetricGroup(8) sage: Groupoid(S8) Groupoid with underlying set Symmetric group of order 8! as a permutation group """
#def construction(self): # return (self.__class__, self.__G)
def _make_named_class_key(self, name): """ The parent/element classes of all groupoids coincide.
EXAMPLES::
sage: Groupoid(DihedralGroup(3)).parent_class is Groupoid(ZZ).parent_class True
"""
def super_categories(self): """ EXAMPLES::
sage: Groupoid(DihedralGroup(3)).super_categories() [Category of sets] """
@classmethod def an_instance(cls): """ Returns an instance of this class.
EXAMPLES::
sage: Groupoid.an_instance() # indirect doctest Groupoid with underlying set Symmetric group of order 8! as a permutation group """ |