From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5864 Path: news.gmane.org!not-for-mail From: Urs Schreiber Newsgroups: gmane.science.mathematics.categories Subject: Re: Straw man terminology Date: Thu, 27 May 2010 10:44:20 +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 X-Trace: dough.gmane.org 1275151182 25087 80.91.229.12 (29 May 2010 16:39:42 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 29 May 2010 16:39:42 +0000 (UTC) To: =?ISO-8859-1?B?Sm95YWwsIEFuZHLp?= Original-X-From: categories@mta.ca Sat May 29 18:39:40 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 1OIP4W-0003Jn-Ct for gsmc-categories@m.gmane.org; Sat, 29 May 2010 18:39:40 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OIOWY-0005Re-PM for categories-list@mta.ca; Sat, 29 May 2010 13:04:35 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5864 Archived-At: Dear Andre, > I agree that Lurie is using the infinity-n-category terminology. > I am not questioning that. > I am observing that he is calling a quasi-category an infinity-category. > In his terminology, an infinity-category is a special kind of > infinity-one-category. > > I believe that the name infinity-category should apply to all "infinity" > categories, > inculding the infinity-one-category. No? Yes, I entirely agree with that. In our discussion I did not promote Jacob Lurie's use of "oo-category" for "quasi-category", What I did and do promote is to use * "oo-groupoid" and "(oo,0)-category" as the term for the abstract concept which is equivalently realized by Kan complexes, simplicial groupoids, topological spaces, etc. and has special strict models by strict omega-groupoids, oo-fold groupoids etc. * "(oo,1)-category" as the term for the abstract concept which is equivalently realized by quasi-categories, Kan-complex enriched categories, complete Segal spaces, Segal categories, categories with weak equivalences, (oo,1)-theta spaces, etc. * "(oo,n)-category" as the term for the abstract concept which is equivalently realized by n-fold complete Segal spaces, (oo,n)-Theta spaces etc. Best, Urs [For admin and other information see: http://www.mta.ca/~cat-dist/ ]