From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5859 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Straw man terminology Date: Wed, 26 May 2010 09:48:16 -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 1274968040 31861 80.91.229.12 (27 May 2010 13:47:20 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 27 May 2010 13:47:20 +0000 (UTC) To: "Urs Schreiber" , Original-X-From: categories@mta.ca Thu May 27 15:47:18 2010 connect(): No such file or directory 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 1OHdQc-0001lE-Kx for gsmc-categories@m.gmane.org; Thu, 27 May 2010 15:47:18 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OHdCU-00068F-My for categories-list@mta.ca; Thu, 27 May 2010 10:32:42 -0300 Thread-Index: Acr8MIAsWVx2GQkHQceName/RuqJVAAqAhbt Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5859 Archived-At: Dear Urs, You wrote: >The term "(infinity,1)-category" is not so much meant as an >alternative for "quasi-category", but as a intentionally less specific >term that subsumes concepts that are different from, but equivalent >to, quasi-categories. Such as Kan-complex-enriched categories or >complete Segal spaces, or algebraic quasi-categories, or categories >with weak equivalences, or... >When doing abstract higher category theory it is useful to be able to >speak, for instance, of the (infinity,1)-category of all small >infinity-groupoids and its abstract properties, without having to >specifically fix a concrete model in terms of which this entity may be >brought to paper. I agree that the terminology (infinity,1)-terminology can be useful. Can I point out that Lurie is calling a quasi-category an = infinity-category? There is a clash of terminology. Best, Andr=E9 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]