From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9351 Path: news.gmane.org!.POSTED!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Cartesian morphism ~~> fibration Date: Wed, 20 Sep 2017 20:53:06 +0930 Message-ID: Reply-To: David Roberts NNTP-Posting-Host: blaine.gmane.org Content-Type: text/plain; charset="UTF-8" X-Trace: blaine.gmane.org 1505927556 31525 195.159.176.226 (20 Sep 2017 17:12:36 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Wed, 20 Sep 2017 17:12:36 +0000 (UTC) To: "categories@mta.ca list" Original-X-From: majordomo@mlist.mta.ca Wed Sep 20 19:12:28 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 1duiXv-0007D9-PO for gsmc-categories@m.gmane.org; Wed, 20 Sep 2017 19:12:23 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43458) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1duiYT-00031i-Ia; Wed, 20 Sep 2017 14:12:57 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1duiWY-00054M-OJ for categories-list@mlist.mta.ca; Wed, 20 Sep 2017 14:10:58 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9351 Archived-At: Dear all, I'm trying to find a reference for the following result, if indeed it is true. Let X1->B and X2->B be fibrations and F:X1->X2 a cartesian functor over B. Then F factors on the nose as X1 -> X1' -> X2 (as functors over B) such that X1->X1' is an equivalence and X1'->X2 is a fibration. I know it is true if X1 and X2 are fibred in groupoids, this construction is in the Stacks Project. But the general case? Thanks, David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]