From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4983 Path: news.gmane.org!not-for-mail From: "Reinhard Boerger" Newsgroups: gmane.science.mathematics.categories Subject: Re: Fundamental Theorem of Category Theory? Date: Wed, 17 Jun 2009 09:29:46 +0200 Message-ID: Reply-To: "Reinhard Boerger" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1245247257 21115 80.91.229.12 (17 Jun 2009 14:00:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 17 Jun 2009 14:00:57 +0000 (UTC) To: "'Ellis D. Cooper'" , Original-X-From: categories@mta.ca Wed Jun 17 16:00:54 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MGvh6-0003hs-Ex for gsmc-categories@m.gmane.org; Wed, 17 Jun 2009 16:00:52 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MGv5P-0000Jp-Qa for categories-list@mta.ca; Wed, 17 Jun 2009 10:21:55 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4983 Archived-At: Dear all, I strongly agree to Ellis Gould's quote of Bill Lawvere's remark on the Yoneda Lemma: > -- a mathematical theory corresponds "roughly to > the definition of a class > of mathematical objects" One of the most important points in category theory are universal properties. The existence of universal solutions is equivalent to the representability of certain functors - at least under reasonable smallness conditions. This is closely related to the Yoneda Lemma; therefore it is really one of the fundamental theorems to me. Greetinge Reinhard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]