From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3976 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: "Historical terminology" Date: Mon, 08 Oct 2007 11:18:42 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019638 11160 80.91.229.2 (29 Apr 2009 15:40:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:38 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Tue Oct 9 00:04:12 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 09 Oct 2007 00:04:12 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1If5I4-0007ja-GV for categories-list@mta.ca; Mon, 08 Oct 2007 23:57:48 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 33 Original-Lines: 38 Xref: news.gmane.org gmane.science.mathematics.categories:3976 Archived-At: Vaughan Pratt wrote: > JeanBenabou wrote: >> (i) Your "guess" about cartesian closed categories is most certainly >> correct. I knew that Eilenberg/Kelly had explicitly used this name >> in their La Jolla paper, and it is probably the first instance, >> because "closed", in this sense, was first introduced in that paper, >> as far as I know.. > > What most impressed my students and me two decades ago, when we were > applying the concepts of EK65 to modeling concurrency, was their attempt > to define "closed" as a self-contained notion independently of any > tensor product as its left adjoint (or so it seemed to us). This > defeated us. Has a clearer story of that attempt, or any related story, > emerged in the meantime? Meanwhile the following examples occurred to me: 1. Implicational logic without conjunction. 2. The type structure of the pure lambda calculus without products. 3. The subcategory of FinSet consisting of the prime powers. (With regard to 3, Mike Barr mentioned to me that (Eilenberg and?) Kelly had come up with the category "-6" meaning the category of all sets save those with six elements, but this seems less natural than the prime powers, important in ideal theory as we saw in the recent discussion about the division lattice.) The free closed category would be a good example if it had ever been sighted in nature? Has it? (Just because we see initial ring every day in the wild doesn't mean that all free objects arise in nature.) Vaughan