From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6565 Path: news.gmane.org!not-for-mail From: "Ellis D. Cooper" Newsgroups: gmane.science.mathematics.categories Subject: Subobject Classifier Algorithm Date: Thu, 03 Mar 2011 10:17:56 -0500 Message-ID: Reply-To: "Ellis D. Cooper" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Trace: dough.gmane.org 1299245757 5945 80.91.229.12 (4 Mar 2011 13:35:57 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 4 Mar 2011 13:35:57 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Fri Mar 04 14:35:53 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 1PvVAe-0004BY-MO for gsmc-categories@m.gmane.org; Fri, 04 Mar 2011 14:35:52 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:41239) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PvVAF-0004td-Lx; Fri, 04 Mar 2011 09:35:27 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PvVAD-000206-2R for categories-list@mlist.mta.ca; Fri, 04 Mar 2011 09:35:25 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6565 Archived-At: 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/ ]