From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5804 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors? Date: Fri, 14 May 2010 11:41:33 -0700 Message-ID: References: <4BEC8698.3090408@ics.mq.edu.au> 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 1273945355 12951 80.91.229.12 (15 May 2010 17:42:35 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 15 May 2010 17:42:35 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Sat May 15 19:42:34 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 1ODLNh-00065N-FC for gsmc-categories@m.gmane.org; Sat, 15 May 2010 19:42:33 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ODKsa-00069O-AC for categories-list@mta.ca; Sat, 15 May 2010 14:10:24 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5804 Archived-At: Michael Batanin wrote: >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. Sorry, but I don't think that you understand what we (Mike and I) mean when we say that "foo" should equal "1-foo". In all of these examples, the word "1-foo" (or "1-tuply foo") means the same as the historic low-dimensional term "foo": * "n-category", with the usual meaning; * "n-set", as you suggested above; * "k-tuply monoidal", as used by John Baez; * "k-braided monoidal", as used by Andre Joyal; * "n-stack", with the usual meaning; * "n-sheaf", as Mike Shulman suggested. In only these examples, the word "1-foo" does ~not~ mean the same as "foo": * "n-connected space", with the usual meaning; * "n-category", with the new meaning that you suggested earlier; * "k-braided monoidal", as you used it here: http://permalink.gmane.org/gmane.science.mathematics.categories/5764/. I like some of the terms in the first list more than others. I find some of them sensibly numbered and some of them not (which is part, but not all, of what goes into my liking them). But I find all of them usable and I instantly understand them. I object to the terms in the second list as inherently confusing, even when I find them sensibly numbered. Of the terms on that list, only "n-connected space" has actually been sanctioned by history. (But see http://ncatlab.org/nlab/show/k-simply+connected+n-category for an alternative approach.) --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]