From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3394 Path: news.gmane.org!not-for-mail From: F W Lawvere Newsgroups: gmane.science.mathematics.categories Subject: Re: Linear--structure or property? Date: Sat, 12 Aug 2006 12:35:47 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019277 8553 80.91.229.2 (29 Apr 2009 15:34:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:34:37 +0000 (UTC) To: "\"Categories\"" Original-X-From: rrosebru@mta.ca Sat Aug 12 20:37:34 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 12 Aug 2006 20:37:34 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GC329-0006Kz-2T for categories-list@mta.ca; Sat, 12 Aug 2006 20:36:49 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 27 Original-Lines: 42 Xref: news.gmane.org gmane.science.mathematics.categories:3394 Archived-At: Beyond simple counter examples to general statements, the Tarski school also pursued conditions on particular monoids which might imply uniqueness of a ring structure, or a definite range of ring structures. As I suggested, that open problem takes on a deeper significance if we consider it within categories of cohesion, not just within the category of abstract sets. Best wishes to all. Bill ************************************************************ On Fri, 11 Aug 2006, George Janelidze wrote: > FW: categories: Re: Linear--structure or property?Dear Florian, > > > 1*2 = f(f(1)+f(2)) = f(1+3) = f(4) = f(2x2) = f(2)xf(2) = 3x3 = 9. > > You are right, and thank you the correction (I think I thought of 3*3 = > f(f(3)+f(3)) = f(2+2) =..., but does not matter of course). > > Dear Bill, > > Having two structures in {0,1} (with 1+1 = 0 and with 1+1 = 1) makes what > you say about the Tarski school funny (sorry!) > > Best regards to all- > > George > > > >