From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5776 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors?= Date: Mon, 10 May 2010 11:16:17 -0700 Message-ID: References: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1273539888 18121 80.91.229.12 (11 May 2010 01:04:48 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 11 May 2010 01:04:48 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Tue May 11 03:04:47 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 1OBdtu-0001JN-Sc for gsmc-categories@m.gmane.org; Tue, 11 May 2010 03:04:47 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBdHV-0002WK-Ur for categories-list@mta.ca; Mon, 10 May 2010 21:25:06 -0300 In-Reply-To: <4BE81F26.4020903@dm.uba.ar> Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5776 Archived-At: Eduardo wrote: > Andre points out: > > "To call a monoidal category 1-braided is kind of confusing because there > is no commutation structure on a general monoidal category. A monoidal > category is 0-braided." > > Being an outsider, with no previous neither usage or opinion on this > terminology beyond just monoidal and/or tensor category, this seems to me > definitive, and more than enough to settle the question. I'm glad that's enough to convince you that Michael Batanin's terminology "monoidal = 1-braided" is inferior to Andre's "monoidal = 0-braided". But I think "braided = doubly monoidal" is even better. After all, a monoidal category has one tensor product; a braided monoidal category has two compatible tensor products, and a symmetric monoidal category has three. But I will not lose sleep if Andre uses "k-braided" as a synonym for "(k+1)-tuply monoidal". I don't see it causing any confusion. I just think it will create more +1's in various formulas. E.g.: the classifying space of a k-braided n-category is a (k+1)-fold loop space. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]