From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4242 Path: news.gmane.org!not-for-mail From: Newsgroups: gmane.science.mathematics.categories Subject: Re: A small cartesian closed concrete category Date: Mon, 03 Mar 2008 16:30:55 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019817 12369 80.91.229.2 (29 Apr 2009 15:43:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:43:37 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Mar 3 20:30:05 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Mar 2008 20:30:05 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JWKrd-00034P-GP for categories-list@mta.ca; Mon, 03 Mar 2008 20:18:37 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 6 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:4242 Archived-At: Peter Easthope points out that in Lawvere & Schanuel there is no mention of Arend Heyting. That is unfortunate, especially since=20 pp 348-352 are devoted to introducing Heyting's Algebras=20 and one of their possible objective origins. The 2nd edition should correct this omission. Summarizing the 16 responses, a common thought of many must=20 have been=20 "If small implies finite then any example must be a poset (category in which any two parallel maps are equal) because of Freyd's theorem. A CC poset is almost=20 by definition a Heying Algebra. There are linearly ordered ones of=20 any size, but if the size is four or more, there are also examples that are not=20 linearly ordered.... =20 On the other hand if infinite examples=20 are allowed, and posetal ones are not, it is hard to think of a CCC smaller than a skeletal category of all finite sets." Bill