From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5908 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Equality and fibration Date: Wed, 2 Jun 2010 10:34:42 +0100 (BST) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE X-Trace: dough.gmane.org 1275485675 10123 80.91.229.12 (2 Jun 2010 13:34:35 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 2 Jun 2010 13:34:35 +0000 (UTC) Cc: Categories list To: =?ISO-8859-15?Q?Joyal=2C_Andr=E9?= Original-X-From: categories@mta.ca Wed Jun 02 15:34:33 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 1OJo5Z-0007T2-Ed for gsmc-categories@m.gmane.org; Wed, 02 Jun 2010 15:34:33 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OJnbe-0006BC-Qm for categories-list@mta.ca; Wed, 02 Jun 2010 10:03:38 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5908 Archived-At: On Mon, 31 May 2010, Joyal, Andr=E9 wrote: > Dear category theorists, > > I have not been able to define the notion of Grothendieck fibration > without using the equality relation between the objects of the base categ= ory. > Can you? > > Andr=E9 > No, because an equivalence of categories is not a Grothendieck fibration in general. However, there is a weaker version of the notion where one replaces equality by the existence of a (specified) isomorphism; there are some comments about this in my paper "Fibrations and partial products in a 2-category" in Applied Categorical Structures 1 (1993), 141--179. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]