From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2815 Path: news.gmane.org!not-for-mail From: "Urs Schreiber" Newsgroups: gmane.science.mathematics.categories Subject: Re: lax crossed modules Date: Wed, 21 Sep 2005 19:06:21 +0200 Message-ID: <012001c5bece$ca12fe70$2846a8c0@acerorzjm7qpwt> References: <001d01c5bd6b$adea7020$94a24e51@brown1> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018921 5929 80.91.229.2 (29 Apr 2009 15:28:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:28:41 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Wed Sep 21 14:45:14 2005 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Sep 2005 14:45:14 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EI8cP-0003vm-SE for categories-list@mta.ca; Wed, 21 Sep 2005 14:42:53 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 24 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:2815 Archived-At: Ronald Brown wrote, in response to David Roberts: > I have a gut feeling that these strengthened sesquicategories (with a > *measure* of the failure of the interchange law) will crop up in a variety > of situations, e.g. in rewriting, 2-dimensional holonomy, ...., since the > interchange law makes things too abelian, sometimes. One can have a 2-holonomy for nonabelian gerbes if a funny condition holds, called the "fake flatness condition", which is a differential version of the exchange law, appearing when one realizes a 2-holonomy in a gerbe as a 2-functor from 2-paths to 2-group 2-torsors. Some people working on bundle gerbes feel that this constraint, which is derived in the context of strict 2-groups (crossed modules) is "too strong". While there are straightforward ways to relax conditions in the formalism, for instance by passing to weak (coherent) structure 2-groups (I guess these are essentially "the same" as lax crossed modules?) this does not seem to really address these people's concerns, because after weakening one no longer deals with Lie groups and Lie algebras, which is what they do. Hence I'd be extremely interested if somebody came up with a nice weakened version of crossed modules that would allow to realize 2-holonomy in non-fake flat gerbes. Best regards, Urs Schreiber