From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5154 Path: news.gmane.org!not-for-mail From: Urs Schreiber Newsgroups: gmane.science.mathematics.categories Subject: Re: 'Directed Algebraic Topology' Date: Mon, 21 Sep 2009 11:44:02 +0200 Message-ID: Reply-To: Urs Schreiber 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: ger.gmane.org 1253541207 12341 80.91.229.12 (21 Sep 2009 13:53:27 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 21 Sep 2009 13:53:27 +0000 (UTC) To: Marco Grandis , categories@mta.ca Original-X-From: categories@mta.ca Mon Sep 21 15:53:20 2009 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 4.50) id 1MpjKR-0001rZ-V9 for gsmc-categories@m.gmane.org; Mon, 21 Sep 2009 15:53:20 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Mpiqk-00049z-24 for categories-list@mta.ca; Mon, 21 Sep 2009 10:22:38 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5154 Archived-At: Marco Grandis wrote: > My book > > =A0 =A0'Directed Algebraic Topology' > =A0 =A0Models of non-reversible worlds > > has appeared, at Cambridge University Press. In that context I am wondering about the following: it would be nice to have a notion of directed topological space that would extend the relation between (nice) topological spaces and oo-groupoids to one between (nice) directed topological spaces and (oo,1)-categories. More generally, it would be nice to have a notion of "r-directed topological space" for r in N that would extend the relation between (nice) topological spaces and oo-groupoids to one of (nice) "r-directed spaces" and (oo,r)-cateories. (Probably such a notion of directed spaces can't be supporrted by plain topological spaces with direction information, but requires filtered directed spaces or the like. ) Has anything like this been considered? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]