From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6290 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: reverting religious terminology Date: Mon, 4 Oct 2010 14:25:20 -0700 Message-ID: References: Reply-To: Michael Shulman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1286281004 10262 80.91.229.12 (5 Oct 2010 12:16:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 5 Oct 2010 12:16:44 +0000 (UTC) Cc: categories@mta.ca To: Thomas Streicher Original-X-From: majordomo@mlist.mta.ca Tue Oct 05 14:16:43 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1P36Rn-0000pr-57 for gsmc-categories@m.gmane.org; Tue, 05 Oct 2010 14:16:43 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:42020) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P36R2-0001dU-Ah; Tue, 05 Oct 2010 09:15:56 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P36Qv-0000HM-8F for categories-list@mlist.mta.ca; Tue, 05 Oct 2010 09:15:49 -0300 In-Reply-To: <20101004193802.GB12769@mathematik.tu-darmstadt.de> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6290 Archived-At: On Mon, Oct 4, 2010 at 12:38 PM, Thomas Streicher wrote: > From http://ncatlab.org/nlab/show/Grothendieck+fibration I take that weak > fibrations are necessary only when considering fibrations in bicategories > that are not 2-categories. Yes, the only reasons I know of for caring about weak fibrations are (1) if you're in a bicategory, or even just in a strict 2-category which lacks the property that weak fibrations can be strictified to strict ones, and (2) to assuage any worries (ideological or otherwise) one might have about the notion of strict fibration not being covariant under equivalence. One bicategory which comes to mind which is not a strict 2-category, and in which I would certainly want to think about internal fibrations, is the bicategory of internal categories and anafunctors in some topos. > Why not take the paradigmatic case of the bicategory Dist of > distributors. Has this exampe been worked out in detail. I don't know; I certainly haven't seen it done. If it hasn't been done, someone should work it out; it might be interesting. Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]