From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6568 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Subobject Classifier Algorithm Date: Fri, 04 Mar 2011 11:44:29 -0200 Message-ID: References: Reply-To: "Eduardo J. Dubuc" 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: dough.gmane.org 1299285565 10393 80.91.229.12 (5 Mar 2011 00:39:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 5 Mar 2011 00:39:25 +0000 (UTC) To: "Ellis D. Cooper" , categories Original-X-From: majordomo@mlist.mta.ca Sat Mar 05 01:39:18 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PvfWg-0006M6-Ga for gsmc-categories@m.gmane.org; Sat, 05 Mar 2011 01:39:18 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:56154) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PvfWP-0000mu-Gx; Fri, 04 Mar 2011 20:39:01 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PvfWM-0004jd-WB for categories-list@mlist.mta.ca; Fri, 04 Mar 2011 20:38:59 -0400 User-Agent: Thunderbird 2.0.0.17 (X11/20080925) In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6568 Archived-At: I copy an old post in the list that may be of interest to the present matter and that I had saved by curiosity but not acted upon afterwards. ________________________________________________________________________ this is to tell, or remind, readers about the Web-based interactive category-theory demonstrations I have on my site. Perhaps of interest to new students now an academic year is starting. They're at http://www.j-paine.org/cgi-bin/webcats/webcats.php . After some preamble, this page contains a form divided into sections. Each section generates a particular construct in the category of finite sets: e.g. a colimit, equaliser, or initial object. You can input sets and arrows, or let the demo choose its own. The output includes a diagram, and text explaining it. Cheers, Jocelyn Paine http://www.j-paine.org +44 (0)7768 534 091 Jocelyn's Cartoons: http://www.j-paine.org/blog/jocelyns_cartoons/ _______________________________________________________________________ greetings e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] Ellis D. Cooper wrote: > P.20 of Prof. Taylor's book briefly recounts the history of > "function" as a (rigorously formulated) expression for numerical > calculation using arithmetic and transcendental operations. More > generally, Cox et al in "Ideals, Varieties, and Algorithms" define > "algorithm" as a (rigorously formulated) set of instructions for > manipulating input expressions resulting in output expressions. > Algorithms may be presented in "pseudocode" as a prelude to > implementation in a particular computer programming language such as > Maple, or Haskell. > > Mac Lane-Moerdijk define an elementary (Lawvere-Tierney) topos to be > a category with finite limits, finite colimits, exponentials, and a > subobject classifier. So to prove a category is a topos it is > necessary to prove that it has a subobject classifier. > > My query was stimulated by Lawvere-Schanuel in "Conceptual > Mathematics" pp.340-341 proof that the category of directed graphs > has a subobject classifier. They give a finite list of the > possibilities for an element of a graph (dot or arrow) to belong to a > subgraph. It seems to me such a list could be generated by an > algorithm. Then there is a step explained by pictures leading to > Omega(DirectedGraph). To me this hints at an algorithm too. > > Ellis D. Cooper > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]