From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4974 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Fundamental Theorem of Category Theory? Date: Mon, 15 Jun 2009 14:58:59 -0700 Message-ID: Reply-To: Vaughan Pratt NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1245170410 24620 80.91.229.12 (16 Jun 2009 16:40:10 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 16 Jun 2009 16:40:10 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Tue Jun 16 18:40:07 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 1MGbhf-0007G7-Gb for gsmc-categories@m.gmane.org; Tue, 16 Jun 2009 18:40:07 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MGb4q-0005vE-W1 for categories-list@mta.ca; Tue, 16 Jun 2009 13:00:01 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4974 Archived-At: Apropos of the Yoneda Lemma, is there some reason why it is usually stated on its own rather than as one direction of a characterization of categories of presheaves on J? Unless I've overlooked or misunderstood something it seems to me that the Yoneda Lemma should state that C is a category of presheaves on J if and only if there exists a full, faithful, and dense functor from J to C. This should generalize the characterization of an Archimedean field as any dense extension of the rationals. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]