From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4951 Path: news.gmane.org!not-for-mail From: Urs Schreiber Newsgroups: gmane.science.mathematics.categories Subject: Re: categories fibered in small categories Date: Mon, 8 Jun 2009 07:13:41 +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: 7bit X-Trace: ger.gmane.org 1244483262 28942 80.91.229.12 (8 Jun 2009 17:47:42 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 8 Jun 2009 17:47:42 +0000 (UTC) To: Andrew Salch , categories@mta.ca Original-X-From: categories@mta.ca Mon Jun 08 19:47:40 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 1MDiwc-00088m-AM for gsmc-categories@m.gmane.org; Mon, 08 Jun 2009 19:47:38 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MDiPi-0007iO-Nq for categories-list@mta.ca; Mon, 08 Jun 2009 14:13:38 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4951 Archived-At: On Sun, Jun 7, 2009 at 1:37 AM, Andrew Salch wrote: > it is well-known (and proven > e.g. in Hollander's PhD thesis) that categories > fibered in groupoids over a small category C > are equivalent to lax presheaves of groupoids on C. [...] >I suspect there is some vast generalization of > this, e.g. with the word "groupoids" replaced by > "quasicategories" or something of that nature, > which somebody has already proven, and in that > case I would prefer to cite the more general result. > Does anyone know if something like this is already > in the literature? Yes, see section 3.3.2 of Jacob Lurie's "Higher Topos Theory" for the statement for "quasicategory valued presheaves". [For admin and other information see: http://www.mta.ca/~cat-dist/ ]