From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9352 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Cartesian morphism ~~> fibration Date: Wed, 20 Sep 2017 19:49:07 +0200 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1506003085 32285 195.159.176.226 (21 Sep 2017 14:11:25 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 21 Sep 2017 14:11:25 +0000 (UTC) Cc: "categories@mta.ca list" To: David Roberts Original-X-From: majordomo@mlist.mta.ca Thu Sep 21 16:11:11 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1dv2C6-0007gu-KR for gsmc-categories@m.gmane.org; Thu, 21 Sep 2017 16:11:10 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43838) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dv2D9-0000F0-61; Thu, 21 Sep 2017 11:12:15 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dv2BF-0001QZ-0I for categories-list@mlist.mta.ca; Thu, 21 Sep 2017 11:10:17 -0300 Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9352 Archived-At: > I'm trying to find a reference for the following result, if indeed it is > true. I think the claim is wrong in general. Let P : X->B be a fibration of categories with a terminal object, i.e. P has a right adjoint right inverse One. Then One : Id_B -> P is a cartesian functor though itself not a fibration in general (e.g. B = 1 and X the ordinal 2 then One picks 1 from 2 which has empty fibre over 0). However, if P is a fibration and Q is a discrete fibration and F is a functor with QF = P then F is a fibration iff F is a cartesian functor from P to Q. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]