From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5788 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors?= Date: Tue, 11 May 2010 20:02:24 -0700 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1273757425 17150 80.91.229.12 (13 May 2010 13:30:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 13 May 2010 13:30:25 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Thu May 13 15:30:24 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 1OCYUY-0007bO-Ih for gsmc-categories@m.gmane.org; Thu, 13 May 2010 15:30:22 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OCXvf-0006gG-DX for categories-list@mta.ca; Thu, 13 May 2010 09:54:19 -0300 Content-Disposition: inline In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5788 Archived-At: Michael Batanin wrote in part: >I agree that it creates some clash in low dimensions but I think it is >not a big deal since classical terminology does not have numbers (nobody >calls a monoidal category 0-braided or symmeteic monoidal category >2-braided monoidal). The low dimensional cases are important but they >are not always good models for higher dimension. As an example, -2 and >-1 categories as Baez and Dolan pointed out can be understood as one >pointed set and two pointed set correspondingly. 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. The concept of n-category makes sense for n as low as -2, so it would be nice to renumber this so that we start at n = 0. However, if we do so, then we need a word other than "-category"; if "category" = "3-category", then this violates "foo" = "1-foo". Similarly, the concept of k-braided MC makes sense for k = -1, so it would be nice to renumber this so that we start at k = 0. However, if we do so, then we need a word other than "-braided MC"; if "braided MC" = "2-braided MC", then this violates "foo" = "1-foo". So either we stick with Andre's numbering, inelegant as may be, or we change Andre's "-braided MC" to John's "-tuply MC". But you say, no, we do not need "foo" = "1-foo", simply renumber so that "braided MC" = "2-braided MC". That is like saying, renumber so that "category" = "3-category". While it is a more elegant numbering, it is likely to be confusing. I will say no more about it. I will be happy to read your papers, as long as you explain your terminology up front, as we all should. I may grumble to myself at your violation of "foo" = "1-foo", but I will nevertheless understand since you have explained. (But if you later post to the categories list about it, then I may be confused if you don't recall the numbering.) --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]