From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6019 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: What else do simplicial sets classify? Date: Sun, 1 Aug 2010 15:16:03 +0100 (BST) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1280752244 6378 80.91.229.12 (2 Aug 2010 12:30:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 Aug 2010 12:30:44 +0000 (UTC) Cc: categories list To: Andrej Bauer Original-X-From: majordomo@mlist.mta.ca Mon Aug 02 14:30:43 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OfuAE-0007rr-J3 for gsmc-categories@m.gmane.org; Mon, 02 Aug 2010 14:30:42 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51655) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Ofu97-0008Qx-D9; Mon, 02 Aug 2010 09:29:33 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Ofu94-0006jt-3I for categories-list@mlist.mta.ca; Mon, 02 Aug 2010 09:29:30 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6019 Archived-At: On Sat, 31 Jul 2010, Andrej Bauer wrote: > The presheaf category of simplicial sets is the classifying topos for > the theory L of a bounded linear order. > > In general, there could be other theories which are "Morita > equivalent" to L in the sense that their classifying toposes are > equivalent to simplicial sets. Are any such known, preferably > occurring in nature? > > With kind regards, > > Andrej > Of course you can write down different presentations for the theory classified by simplicial sets; any set of generators for the topos will give you one. But you're unlikely to find anything familiar: if there were a geometric theory "occurring in nature" whose category of models (in any topos) was equivalent to the category of bounded linear orders, that equivalence would almost certainly be well known. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]