From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5796 Path: news.gmane.org!not-for-mail From: Michael Batanin Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors?= Date: Fri, 14 May 2010 09:09:12 +1000 Message-ID: References: Reply-To: Michael Batanin NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1273843345 3174 80.91.229.12 (14 May 2010 13:22:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 14 May 2010 13:22:25 +0000 (UTC) To: Toby Bartels Original-X-From: categories@mta.ca Fri May 14 15:22:24 2010 connect(): No such file or directory 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 4.69) (envelope-from ) id 1OCuqO-0003mI-9v for gsmc-categories@m.gmane.org; Fri, 14 May 2010 15:22:24 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OCuOg-0002Wv-Kb for categories-list@mta.ca; Fri, 14 May 2010 09:53:46 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5796 Archived-At: >> Should we shift the >> numbers and call category a 3-category? > > No, but it seems to me that you are doing something very much like this. Not at all. It may be was not a good example. A better example would be categories. If we follow the principle "foo = 1 foo" and want to agree with historical low dimensional terminology we should call categories 2-sets. Set = 1 Set. So, categories = 2 Set. Nobody will do it I guess. There are many other examples like stack, gerbes and so on. I agree with Mike Shulman that this is a byproduct of categorification. But we can survive with it. Concerning n-braided categories versus (n+1)-fold categories. Yes, I would be happy to use (n+1)-fold terminology but it also clashes with iterated monoidal categories of BFSW as I said. Michael. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]