From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5538 Path: news.gmane.org!not-for-mail From: "Hans-Peter Stricker" Newsgroups: gmane.science.mathematics.categories Subject: Re: Examples for the Yoneda lemma Date: Fri, 15 Jan 2010 13:50:20 +0100 Message-ID: References: <46ffa45f1001150307r793d81c6s7963324885fba107@mail.gmail.com> Reply-To: "Hans-Peter Stricker" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed;charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1263599151 28165 80.91.229.12 (15 Jan 2010 23:45:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 15 Jan 2010 23:45:51 +0000 (UTC) To: "Aleks Kissinger" , Original-X-From: categories@mta.ca Sat Jan 16 00:45:43 2010 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 1NVvrJ-0006kE-8Z for gsmc-categories@m.gmane.org; Sat, 16 Jan 2010 00:45:41 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NVvVn-0003zJ-8e for categories-list@mta.ca; Fri, 15 Jan 2010 19:23:27 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5538 Archived-At: Hello Aleks, I am not quite what to think of the poset of unlabeled graphs without isolated vertices with the relation of embeddability: I have the feeling, that such a graph is NOT completely determined by its set of in-arrows (see http://epublius.de/Fragment_of_the_category_of_unlabeled_graphs_without_isolated_vertices.pdf to see what I mean, e.g. vertices 3 and 4 or vertices 7,8,9). Do I miss something? Best Hans-Peter ----- Original Message ----- From: "Aleks Kissinger" To: "Hans-Peter Stricker" Cc: Sent: Friday, January 15, 2010 12:07 PM Subject: Re: categories: Examples for the Yoneda lemma > The simplest example I can think of is posets. If you represent a > poset as a category (i.e. a category with at most one arrow from A->B > such that A->B and B->A implies A=B), then an object A is completely > determined by the set of arrows going in to it. > > In this context, the Yoneda embedding is the familiar result that any > poset P embeds fully and faithfully in the powerset of P, ordered by > subset inclusion. > > > Aleks [For admin and other information see: http://www.mta.ca/~cat-dist/ ]