From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5844 Path: news.gmane.org!not-for-mail From: Urs Schreiber Newsgroups: gmane.science.mathematics.categories Subject: Re: Straw man terminology Date: Mon, 24 May 2010 15:07:09 +0200 Message-ID: References: Reply-To: Urs Schreiber NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1274808424 1073 80.91.229.12 (25 May 2010 17:27:04 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 25 May 2010 17:27:04 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Tue May 25 19:27:01 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 1OGxu9-0004VQ-Bo for gsmc-categories@m.gmane.org; Tue, 25 May 2010 19:27:01 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OGxGz-00013E-4k for categories-list@mta.ca; Tue, 25 May 2010 13:46:33 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5844 Archived-At: > I also like Andre's term ``quasi-categories'' and prefer it to the > infinity alternatives, for the reasons he gives. Like Kan complex, > it has a fixed and evocative definite meaning, unlikely to be confused > with anything else. 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. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]