From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6884 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Simplicial groups are Kan Date: Mon, 12 Sep 2011 10:35:10 +0100 Message-ID: References: Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1315875116 7319 80.91.229.12 (13 Sep 2011 00:51:56 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 13 Sep 2011 00:51:56 +0000 (UTC) Cc: Categories list To: Michael Barr Original-X-From: majordomo@mlist.mta.ca Tue Sep 13 02:51:52 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R3HE7-0000Cv-PB for gsmc-categories@m.gmane.org; Tue, 13 Sep 2011 02:51:52 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39942) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R3HCt-0008Ec-Tn; Mon, 12 Sep 2011 21:50:35 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R3HCt-0003mU-6g for categories-list@mlist.mta.ca; Mon, 12 Sep 2011 21:50:35 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6884 Archived-At: The reference is included in this review *MR1173825 *of the cubical case. Tonks, A. P.=20 (4-NWAL)=20 Cubical groups which are Kan. /J. Pure Appl. Algebra/=20 =20 81=20 (1992),=20 no.=20 1,=20 =20 83=9687.=20 =20 The author shows that group objects in the category of cubical sets with=20 connections [R. Brown and P. J. Higgins, J. Pure Appl. Algebra 21=20 (1981), no. 3, 233--260; MR0617135 (82m:55015a)=20 ]=20 satisfy the Kan extension condition. This is a very nice correspondence=20 with the simplicial case [J. C. Moore, in S=E9minaire Henri Cartan de=20 l'Ecole Normale Sup=E9rieure, 1954/1955, Exp. No. 18, Secr=E9tariat Math.= ,=20 Paris, 1955; see MR0087934 (19,438e)=20 ].=20 Ronnie On 12/09/2011 01:30, Michael Barr wrote: > I know that is a theorem, due I think to John Moore. Can anyone give me= a > pointer to the original article. > > Michael > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]