From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4975 Path: news.gmane.org!not-for-mail From: "Ellis D. Cooper" Newsgroups: gmane.science.mathematics.categories Subject: Fundamental Theorem of Category Theory? Date: Mon, 15 Jun 2009 18:02:53 -0400 Message-ID: Reply-To: "Ellis D. Cooper" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Trace: ger.gmane.org 1245170926 26290 80.91.229.12 (16 Jun 2009 16:48:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 16 Jun 2009 16:48:46 +0000 (UTC) To: Makoto Hamana ,categories@mta.ca Original-X-From: categories@mta.ca Tue Jun 16 18:48:44 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 1MGbpz-0002a5-6f for gsmc-categories@m.gmane.org; Tue, 16 Jun 2009 18:48:43 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MGbBF-0006VM-UM for categories-list@mta.ca; Tue, 16 Jun 2009 13:06:37 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4975 Archived-At: Dear Makoto, At 11:08 AM 6/14/2009, you wrote: >I don't know how much Yoneda Lemma is useful in other areas of >mathematics, and >I have wanted to know it. The Yoneda Lemma came to mind partly because of M. Barr and C. Wells book "Toposes, Triples and Theories." Its Preface recounts that in the sense of Lawvere's insight -- a mathematical theory corresponds "roughly to the definition of a class of mathematical objects" -- toposes, triples, and theories are beautifully connected fundamental notions. Barr-Wells write that the Yoneda Embeddings Theorem, "the first of several important consequences" of the Yoneda Lemma, "in one way or another is used in practically every mathematical argument in this book." (p. 27) Perhaps subscribers to this list would care to comment on how specific results in this book apply or relate to computer science, other areas of mathematics, logic, or physics. All the best, Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]