From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7829 Path: news.gmane.org!not-for-mail From: "Noson S. Yanofsky" Newsgroups: gmane.science.mathematics.categories Subject: Re: Higher Lawvere theories? Date: Sat, 3 Aug 2013 23:08:26 -0400 Message-ID: Reply-To: "Noson S. Yanofsky" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1375623097 32006 80.91.229.3 (4 Aug 2013 13:31:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 4 Aug 2013 13:31:37 +0000 (UTC) To: "'Categories list'" Original-X-From: majordomo@mlist.mta.ca Sun Aug 04 15:31:37 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 1V5yPD-00080a-Um for gsmc-categories@m.gmane.org; Sun, 04 Aug 2013 15:31:32 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58395) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1V5yO2-0000Qa-Ks; Sun, 04 Aug 2013 10:30:18 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1V5yO1-00076I-Tm for categories-list@mlist.mta.ca; Sun, 04 Aug 2013 10:30:17 -0300 Content-Language: en-us Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7829 Archived-At: Hi, In a paper: Coherence, Homotopy and 2-Theories K-Theory 23: Pgs 203 - 235. (2001). I worked out much of 2-Theories and their relationship with coherence theory. Abstract: 2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a Quillen model category structure on the category of 2-theories and 2-theory-morphisms where the weak equivalences are biequivalences of 2-theories. A biequivalence of 2-theories (Morita equivalence) induces and is induced by a biequivalence of 2-categories of algebras. This model category structure allows one to talk of the homotopy of 2-theories and discuss the universal properties of coherence. There is also a version on the arXiv: http://xxx.lanl.gov/abs/math.CT/0007033 All the best, Noson Yanofsky -----Original Message----- From: Mike Stay [mailto:metaweta@gmail.com] Sent: Friday, August 02, 2013 12:35 PM To: categories Subject: categories: Higher Lawvere theories? 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/ ]