From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3978 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Help! Date: Mon, 08 Oct 2007 08:43:15 -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 1241019640 11167 80.91.229.2 (29 Apr 2009 15:40:40 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:40 +0000 (UTC) To: Categories list 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 1If5GP-0007dN-MU for categories-list@mta.ca; Mon, 08 Oct 2007 23:56:05 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 35 Original-Lines: 13 Xref: news.gmane.org gmane.science.mathematics.categories:3978 Archived-At: > (It helps to know ahead of time what answers are likely; > fortunately there were no pure number theorists at my school.) At the risk of sounding like a cracked record, how about the division category in lieu of the division lattice, namely the coproduct completion of the set P of primes as a discrete category? For a longer story use P* instead of P, P with a final object adjoined. Motivate the division category by pointing out that only the square-free positive integers can be recovered as sups of primes in the division lattice. Vaughan