From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4973 Path: news.gmane.org!not-for-mail From: Makoto Hamana Newsgroups: gmane.science.mathematics.categories Subject: Re: Fundamental Theorem of Category Theory? Date: Mon, 15 Jun 2009 00:08:58 +0900 (JST) Message-ID: Reply-To: Makoto Hamana NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (generated by tm-edit 7.100) Content-Type: text/plain; charset=US-ASCII X-Trace: ger.gmane.org 1245102246 2496 80.91.229.12 (15 Jun 2009 21:44:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 15 Jun 2009 21:44:06 +0000 (UTC) To: categories , "Ellis D. Cooper" Original-X-From: categories@mta.ca Mon Jun 15 23:44:04 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 1MGJyG-0007YF-6v for gsmc-categories@m.gmane.org; Mon, 15 Jun 2009 23:44:04 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MGJJ5-0005up-FN for categories-list@mta.ca; Mon, 15 Jun 2009 18:01:31 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4973 Archived-At: Dear Ellis, On Fri, 5 June 2009 16:36:23 -0400, Ellis D. Cooper wrote: | There are Fundamental Theorems of Arithmetic, Algebra, Calculus, and | indeed, many more. | My question is, What would be candidates for the Fundamental Theorem | of Category Theory? | Yoneda Lemma comes to my mind. What do you think? I have asked Prof. Yoneda many years ago why Yoneda Lemma is called "Lemma", not "Theorem". He said that perhaps it was a bit about internal of category theory rather than insisting on applications to other mathematics. Doesn't Yoneda Lemma satisfy (c) in Mile Gould's post? I don't know how much Yoneda Lemma is useful in other areas of mathematics, and I have wanted to know it. On Sat, 6 June 2009 23:22:52 +0100, Miles Gould wrote: | My suggestion would be the theorem that left adjoints preserve colimits, | and right adjoints preserve limits. | This may not be the deepest theorem in category theory, but | (a) it's pretty darn deep, | (b) it describes a beautiful connection between two fundamental notions | in the subject, | (c) it admits a huge variety of applications in "ordinary" mathematics. Best Regards, Makoto Hamana [For admin and other information see: http://www.mta.ca/~cat-dist/ ]