From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6029 Path: news.gmane.org!not-for-mail From: Alex Hoffnung Newsgroups: gmane.science.mathematics.categories Subject: Spans in Bicategories Date: Mon, 2 Aug 2010 21:10:37 -0400 Message-ID: Reply-To: Alex Hoffnung NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1280916739 22254 80.91.229.12 (4 Aug 2010 10:12:19 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 4 Aug 2010 10:12:19 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Aug 04 12:12:18 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 1OgaxM-00083x-Ht for gsmc-categories@m.gmane.org; Wed, 04 Aug 2010 12:12:16 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50176) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OgauP-0002u5-Li; Wed, 04 Aug 2010 07:09:13 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OgauG-0006xd-Vy for categories-list@mlist.mta.ca; Wed, 04 Aug 2010 07:09:05 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6029 Archived-At: Hello all, In Benabou's 1967 paper, he gives the bicategory of spans in a category with pullbacks as an example of a bicategory. It seems to be fairly common knowledge that spans in a bicategory with weak pullbacks form a tricategory (or a bicategory if appropriate isomorphism classes are taken or fibrations required). If the bicategory has finite limits there should be a monoidal structure as well. I know people use these results fairly often, at least at the level of monoidal bicategories, but does anyone know if there exists a written account of such a theorem? Best, Alex Hoffnung [For admin and other information see: http://www.mta.ca/~cat-dist/ ]