From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6020 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: What else do simplicial sets classify? Date: Sun, 1 Aug 2010 13:14:39 -0400 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1280752340 6785 80.91.229.12 (2 Aug 2010 12:32:20 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 Aug 2010 12:32:20 +0000 (UTC) To: "Andrej Bauer" , "categories list" Original-X-From: majordomo@mlist.mta.ca Mon Aug 02 14:32:19 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OfuBl-00008y-9d for gsmc-categories@m.gmane.org; Mon, 02 Aug 2010 14:32:17 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44585) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OfuAL-0003gC-4B; Mon, 02 Aug 2010 09:30:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OfuAI-0006lW-BP for categories-list@mlist.mta.ca; Mon, 02 Aug 2010 09:30:46 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6020 Archived-At: Dear Andrej, I do not know what you mean by a bounded linear order. But I know that the topos of simplicial sets is classifying strict intervals. (an interval [a,b] is strict if its endpoint a and b are different) bounded linear orders =3D strict intervals? Best,=20 Andr=E9 -------- Message d'origine-------- De: Andrej Bauer [mailto:andrej.bauer@andrej.com] Date: sam. 31/07/2010 03:55 =C0: categories list Objet : categories: What else do simplicial sets classify? =20 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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]