From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6890 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Another question about Kan Date: Tue, 13 Sep 2011 10:28:22 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1315963057 16975 80.91.229.12 (14 Sep 2011 01:17:37 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 14 Sep 2011 01:17:37 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Wed Sep 14 03:17:32 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 1R3e6V-0002kA-PI for gsmc-categories@m.gmane.org; Wed, 14 Sep 2011 03:17:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:36877) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R3e5M-0006vh-O0; Tue, 13 Sep 2011 22:16:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R3czl-0007yj-Of for categories-list@mlist.mta.ca; Tue, 13 Sep 2011 21:06:29 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6890 Archived-At: Is the following known? An equational category has the property that every simplicial object is Kan iff it is a Mal'cev category. This means that there is a ternary operation I call <-,-,-> such that = x and = y. In a sense this is not surprising. The Kan condition makes homotopy an equivalence relation. The degeneracies make homotopy reflexive and Mal'cev categories are characterized by the fact that every reflexive binary relation is an equivalence relation. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]