From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5471 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Small is beautiful Date: Mon, 04 Jan 2010 00:41:13 -0800 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1262659688 10573 80.91.229.12 (5 Jan 2010 02:48:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 5 Jan 2010 02:48:08 +0000 (UTC) To: categories list Original-X-From: categories@mta.ca Tue Jan 05 03:48:00 2010 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 4.50) id 1NRzSh-0002Ha-F6 for gsmc-categories@m.gmane.org; Tue, 05 Jan 2010 03:47:59 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NRyym-0007V7-AB for categories-list@mta.ca; Mon, 04 Jan 2010 22:17:04 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5471 Archived-At: Ross Street wrote: > Part of what Bob Par=E9 was arguing, I believe, was that we should be=20 > flexible > (pun intended) about what "small" means. If "small" means "finite" then= =20 > FinSet > is not "essentially small". Also, "small" could mean "no more than one=20 > element". Thanks, Ross. Hopefully Bob will phrase it that way next time. ;) If 2 is the usual symmetric monoidal closed category with objects 0 and=20 1 and only non-identity morphism 0 --> 1, then Chu(2,1) has four objects=20 while Chu(2,0) has only three, but both are self-dual. The CEO of=20 search engine company Cuil (Old Irish for knowledge) had finite=20 categories of this kind in her 1997 Ph.D. thesis. What got me started on my previous message was that Bob was calling=20 these "syntactic" when to me they were semantic. If by "syntactic" he=20 meant "finite," or more generally less than some specified ordinal, then=20 I have no problem with that, other than that I'd prefer he be specific=20 about the ordinal rather than vaguely saying "syntactic." Vaughan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]