From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4212 Path: news.gmane.org!not-for-mail From: Paul Taylor Newsgroups: gmane.science.mathematics.categories Subject: Re: A small cartesian closed concrete category Date: Fri, 15 Feb 2008 08:18:57 +0000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v624) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019796 12233 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: categories@mta.ca 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 1JQ1i2-0006co-PZ for categories-list@mta.ca; Fri, 15 Feb 2008 10:38:38 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 34 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:4212 Archived-At: Peter Easthope asked, > Is there a cartesian closed concrete category which > is small enough to write out explicitly? It would be > helpful in learning about map objects, exponentiation, > distributivity and etc. Can such a category be made > with binary numbers for instance? How about finite sets and functions? Not just a CCC but an elementary topos. I'm not sure what you mean by "binary numbers", but the powerset of n is 2^n (I wonder why Cantor introduced this notation?), and the subsets of n are n-digit binary numbers. As for more general function spaces, maybe it's worth an undergraduate exercise to see whether there's a neat representation. NBB: You don't need even to have heard of domain theory to find examples of CCCs! Paul Taylor