From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4211 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: A small cartesian closed concrete category Date: Thu, 14 Feb 2008 22:46:44 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019796 12232 80.91.229.2 (29 Apr 2009 15:43:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:43:16 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Fri Feb 15 10:43:09 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 15 Feb 2008 10:43:09 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JQ1hV-0006Xq-7n for categories-list@mta.ca; Fri, 15 Feb 2008 10:38:05 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 33 Original-Lines: 25 Xref: news.gmane.org gmane.science.mathematics.categories:4211 Archived-At: On Thu, 14 Feb 2008 10:07:27 PM EST, PETER EASTHOPE asked: > Is there a cartesian closed concrete category which > is small enough to write out explicitly? = How about the full category of finite sets? Or, = if that's not small enough, and you really fancy an example > ... made with binary numbers for instance , try the skeletal version of the full category of "sets of cardinality < 2= " having as only objects the ordinal numbers 0 and 1. Here 0 x A =3D 0, 1 x A =3D A, 0^1 =3D 0, 0^0 =3D 1, 1^A =3D 1. In other words, B x A =3D min(A, B), B^A =3D max(1-A, B). Happy Valentines's Day! -- Fred