From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5288 Path: news.gmane.org!not-for-mail From: Zinovy Diskin Newsgroups: gmane.science.mathematics.categories Subject: double fibrations Date: Mon, 16 Nov 2009 12:41:34 -0500 Message-ID: Reply-To: Zinovy Diskin NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1258417225 8570 80.91.229.12 (17 Nov 2009 00:20:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 17 Nov 2009 00:20:25 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Tue Nov 17 01:20:18 2009 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 4.50) id 1NABnr-0003UZ-6x for gsmc-categories@m.gmane.org; Tue, 17 Nov 2009 01:20:15 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NABPs-0006qy-LP for categories-list@mta.ca; Mon, 16 Nov 2009 19:55:28 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5288 Archived-At: Dear Categories, I'd appreciate references on the following construction. Let f: E-->B be a double functor between double categories (mapping 2-,1-,0-cels in E to the respective cells in B); and let me call squares double-arrows and write them as D: S==>T with S a span (h:B<-- A-->A':u) and T a cospan (h':A'-->B'<--B:v) with h,h' being horizontal and u,v vertical arrows. Functor f is called a double fibration if for any double-arrow D: S==>T in B and a span t over T in E, there is a suitably defined Cartesian lifting d:s=>t of D. I'm also interested in mixed lifting being fibrational for horizontal and opfibrational for vertical arrows. Did anybody study such things? Or writing it down would be straightforward? Thanks, Zinovy [For admin and other information see: http://www.mta.ca/~cat-dist/ ]