From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3927 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: unital weak functor? Date: Thu, 20 Sep 2007 09:01:21 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019609 10944 80.91.229.2 (29 Apr 2009 15:40:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:09 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Sep 20 18:07:45 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Sep 2007 18:07:45 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IYT6d-0006up-Ox for categories-list@mta.ca; Thu, 20 Sep 2007 17:58:39 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 51 Original-Lines: 41 Xref: news.gmane.org gmane.science.mathematics.categories:3927 Archived-At: Josh Nichols-Barrer wrote: > Hi everyone, > > Is there a name for a weak functor between bicategories which takes > identity 1-morphisms to identity 1-morphisms? "Unital weak functor" > would > seem an apt name, but if there is another with more precedent I'll just > use that instead. I don't think there's a standard term. But, I like the term "normalized", since in certain circumstances weak functors between bicategories are described by cocycles in group cohomology, and the cocycle is then said to be "normalized" when the weak functor preserves identity 1-morphisms. It's an old fact that every cocycle is equivalent to a normalized one, and this is related to the fact that every weak functor is isomorphic to a normalized one. For more information on this, see: Andre Joyal and Ross Street, Braided monoidal categories, Macquarie Mathematics Report No. 860081, November 1986. Also available at http://rutherglen.ics.mq.edu.au/~street/JS86.pdf or for a pedagogical treatment, try section 8.3, "Classifying 2-groups using group cohomology", of this: John Baez and Aaron Lauda, Higher-dimensional algebra V: 2-Groups, Theory and Applications of Categories 12 (2004), 423-491. Also available at http://arxiv.org/abs/math.QA/0307200 Best, jb