From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4987 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Fundamental Theorem of Category Theory? Date: Wed, 17 Jun 2009 13:04:56 -0400 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1245282886 18256 80.91.229.12 (17 Jun 2009 23:54:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 17 Jun 2009 23:54:46 +0000 (UTC) To: Original-X-From: categories@mta.ca Thu Jun 18 01:54:44 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 1MH4xj-0007Vq-Pf for gsmc-categories@m.gmane.org; Thu, 18 Jun 2009 01:54:39 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MH4Nj-0005uD-3Q for categories-list@mta.ca; Wed, 17 Jun 2009 20:17:27 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4987 Archived-At: Once, long, long ago, I looked up the Yoneda paper = then cited as source for the Y.L. = Agreed: not there. = But, in another Yoneda paper ("On Ext and exact sequences", perhaps, I'm relying on memory alone, here), it *is* there, not called Y.L., of course, but describing, as I recall, = the connection between n.t.(hom(A, -), hom(B, -)) and = hom(B, A) in the case that the hom-sets are the = Ext equivalence classes (the only case of interest = for that paper). It didn't take much, either, to see the underlying = Y.L. structure in the main proof there. Cheers (and more detail, if called for, once I'm back from Montrreal), = -- Fred ------ Original Message ------ Received: Wed, 17 Jun 2009 09:22:42 AM EDT From: "Prof. Peter Johnstone" To: Makoto Hamana , Subject: categories: Re: Fundamental Theorem of Category Theory? > On Mon, 15 Jun 2009, Makoto Hamana wrote: > = > > 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. > > > When I lecture on category theory to first-year graduate students, I > tell them there are two things they should remember about the > Yoneda Lemma: it isn't a lemma, and it was never published by Yoneda. > In this respect it resembles that bulwark of the British constitution, > the Lord Privy Seal (who is none of the three things that his title > claims). > = > Peter Johnstone > = [For admin and other information see: http://www.mta.ca/~cat-dist/ ]