From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7827 Path: news.gmane.org!not-for-mail From: Aleks Kissinger Newsgroups: gmane.science.mathematics.categories Subject: Re: Higher Lawvere theories? Date: Sat, 3 Aug 2013 14:47:37 +0100 Message-ID: References: Reply-To: Aleks Kissinger NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1375623018 31303 80.91.229.3 (4 Aug 2013 13:30:18 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 4 Aug 2013 13:30:18 +0000 (UTC) Cc: categories To: Mike Stay Original-X-From: majordomo@mlist.mta.ca Sun Aug 04 15:30:21 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1V5yO1-0004uy-S3 for gsmc-categories@m.gmane.org; Sun, 04 Aug 2013 15:30:17 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58383) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1V5yLy-0000Ck-Vf; Sun, 04 Aug 2013 10:28:10 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1V5yLy-000740-5a for categories-list@mlist.mta.ca; Sun, 04 Aug 2013 10:28:10 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7827 Archived-At: The strict case has been studied quite a bit using n-polygraphs (aka computads), which give a way of presenting an n-category by generators and relations (where relations are given by n+1 dimensional cells). Often the concern is decidablility of the (higher-dimensional) word problem, using rewriting. They originally came out of work by Street and Burroni. More recently, Yves Guiraud has written about them quite extensively. See e.g.: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.144.3106&rep=rep1&type=pdf Best, Aleks Kissinger On 2 August 2013 17:35, Mike Stay wrote: > Has anyone worked out the details of "higher Lawvere theories" so that > one can say "the free bicategory on this object, these morphisms, > these 2-morphisms, modulo these equations of 2-morphisms"? > -- > Mike Stay - metaweta@gmail.com > http://www.cs.auckland.ac.nz/~mike > http://reperiendi.wordpress.com > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]