From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8153 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: Composition of Fibrations and Quantification Date: Sun, 8 Jun 2014 14:58:38 +0100 Message-ID: References: Reply-To: Steve Vickers NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (1.0) Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1402360874 9665 80.91.229.3 (10 Jun 2014 00:41:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 10 Jun 2014 00:41:14 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Tue Jun 10 02:41:08 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1WuA7g-0004Ni-D8 for gsmc-categories@m.gmane.org; Tue, 10 Jun 2014 02:41:08 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:35098) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1WuA6x-00054a-Ks; Mon, 09 Jun 2014 21:40:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1WuA6x-0004vo-DA for categories-list@mlist.mta.ca; Mon, 09 Jun 2014 21:40:23 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8153 Archived-At: Some thoughts: * The result about composition of fibrations holds in any 2-category with co= mma objects and 2-pullbacks, not just Cat. (Think of the Chevalley criterion= for fibrations.) * By duality on 2-cells it thus also applies to opfibrations, and hence to b= ifibrations. * It is bifibration structure that gives you the left adjoints you ask for. * For the right adjoints, look at the dual 2-category, where your fibrations= become bifibrations. Hence it seems to me that your conjectures are all true, and even generalize= widely. Steve. > On 6 Jun 2014, at 10:47, Neil Ghani wrote: >=20 > Dear All >=20 > We know that if p and q are fibrations, then their composition p.q is a fi= bration. >=20 > But what about quantification =E2=80=A6 that is if reindexing along every m= orphism has a right/left adjoint in p and q, then does reindexing along ever= y morphism in p.q have a right/left adjoint? Under some circumstances? >=20 > Thanks for any thoughts > Neil [For admin and other information see: http://www.mta.ca/~cat-dist/ ]