From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5655 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: equality is beautiful Date: Mon, 22 Mar 2010 11:15:25 -0500 Message-ID: References: Reply-To: Michael Shulman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-7 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1269397164 10665 80.91.229.12 (24 Mar 2010 02:19:24 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 24 Mar 2010 02:19:24 +0000 (UTC) Cc: categories@mta.ca To: Toby Bartels Original-X-From: categories@mta.ca Wed Mar 24 03:19:19 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 1NuGBj-0003Dn-FF for gsmc-categories@m.gmane.org; Wed, 24 Mar 2010 03:19:19 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NuFi2-0000s6-P5 for categories-list@mta.ca; Tue, 23 Mar 2010 22:48:38 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5655 Archived-At: On Sun, Mar 21, 2010 at 2:36 PM, Toby Bartels wrote: > The elements of identity types have their own identity types, etc, > so every type becomes not only a set but an infinity-groupoid; > see Awodey & Warren's paper at http://arxiv.org/abs/0709.0248 > and Michael Warren's PhD thesis at http://aix1.uottawa.ca/~mwarren/Papers= / I think maybe the papers you wanted to refer to for that fact are Benno van den Berg and Richard Garner, Types are weak =F9-groupoids, arXiv:0812.0298 Peter Lumsdaine, Weak =F9-categories from intensional type theory, arXiv:08= 12.0409 The Awodey+Warren papers are about the other direction, that type theory with identity types can be interpreted in any well-enough-behaved model category. I agree, though, that identity types vitiate the goal of doing category theory without a notion of equality for objects. Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]