From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5630 Path: news.gmane.org!not-for-mail From: Chris Heunen Newsgroups: gmane.science.mathematics.categories Subject: Re: zigzag category Date: Wed, 10 Mar 2010 09:16:23 -0800 Message-ID: References: Reply-To: Chris Heunen NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1268276120 13644 80.91.229.12 (11 Mar 2010 02:55:20 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 11 Mar 2010 02:55:20 +0000 (UTC) Cc: categories@mta.ca To: Paul Levy Original-X-From: categories@mta.ca Thu Mar 11 03:55:16 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 1NpYYM-00064y-GD for gsmc-categories@m.gmane.org; Thu, 11 Mar 2010 03:55:14 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NpY6h-0005Lu-Ci for categories-list@mta.ca; Wed, 10 Mar 2010 22:26:39 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5630 Archived-At: Dear Paul, My PhD thesis covers a construction for dagger categories in 3.1.18 and further that is slightly different but related; at least I also called this functor Zigzag:Cat->DagCat. In that case, it is left adjoint to the evident forgetful functor. best, Chris > 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/ ]