From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5623 Path: news.gmane.org!not-for-mail From: Paul Levy Newsgroups: gmane.science.mathematics.categories Subject: zigzag category Date: Tue, 9 Mar 2010 15:12:04 +0000 Message-ID: Reply-To: Paul Levy NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1268223046 26494 80.91.229.12 (10 Mar 2010 12:10:46 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 10 Mar 2010 12:10:46 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Mar 10 13:10:42 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1NpKkH-0002R3-A3 for gsmc-categories@m.gmane.org; Wed, 10 Mar 2010 13:10:37 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NpK7a-0000ig-70 for categories-list@mta.ca; Wed, 10 Mar 2010 07:30:38 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5623 Archived-At: For a set A, let Cat(A) be the category whose objects are small categories with object set A, and whose morphisms are identity-on- objects functors. For a small category C, let zigzag(C) be the coproduct of C and C^op within Cat(ob C). Explicitly, in zigzag(C), a non-identity morphism z : a ---> b is a nonempty sequence of non-identity C-morphisms that alternately go forwards or backwards. Depending on the direction of the first and last C-morphism, z can take one of four different forms. Surely this appears in the literature? Google gave me a zillion categorical papers that mention zigzags, but I didn't find this construction, although several were close (e.g. the special case where C is the free category on a graph). Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]