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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() 

""" 

CategoryWithParameters.__init__(self) #, "Groupoid") 

if G is None: 

from sage.groups.perm_gps.permgroup_named import SymmetricGroup 

G = SymmetricGroup(8) 

self.__G = G 

 

def _repr_(self): 

""" 

EXAMPLES:: 

 

sage: S8 = SymmetricGroup(8) 

sage: Groupoid(S8) 

Groupoid with underlying set Symmetric group of order 8! as a permutation group 

""" 

return "Groupoid with underlying set %s"%self.__G 

 

#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 

 

""" 

return None 

 

def super_categories(self): 

""" 

EXAMPLES:: 

 

sage: Groupoid(DihedralGroup(3)).super_categories() 

[Category of sets] 

""" 

return [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 

""" 

from sage.groups.perm_gps.permgroup_named import SymmetricGroup 

G = SymmetricGroup(8) 

return cls(G)