From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5771 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax monoidal functors Date: Mon, 10 May 2010 09:12:58 -0700 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1273539838 18000 80.91.229.12 (11 May 2010 01:03:58 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 11 May 2010 01:03:58 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Tue May 11 03:03:56 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 1OBdt5-00014z-6l for gsmc-categories@m.gmane.org; Tue, 11 May 2010 03:03:55 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBdE1-0002OI-E4 for categories-list@mta.ca; Mon, 10 May 2010 21:21:29 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5771 Archived-At: Michael Batanin wrote: >Dear John and Andre, >I am using a mixture of your terminologies: > monoidal =3D 1-braided > braided =3D 2-braided > sylleptic =3D 3-braided >...... I think that this terminology is dangerous. While there is a debate to be had over which is better: John's "k-tuply monoidal" or Andr=E9's "k-braided monoidal", the good thing about either of them is that you can understand them without having to be told precisely how the numbering works, as long as you follow the rule that "1-foo" =3D "foo". So while I also prefer John's numbering to Andr=E9's, I'm happy to use either and have had occasion to use both. But mixing John's numbering with Andr=E9's terminology would confuse me. Sometimes the "1-foo" =3D "foo" rule is violated. I was very confused when I first saw "n-connected space"; I'd have understood "n-simply connected space" right away. I tend to think that a lot of established names are badly numbered, including "n-category" which may be the most basic on a categories list, but it doesn't really cause any problems as long as "1-foo" =3D "foo". --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]