From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6686 Path: news.gmane.org!not-for-mail From: Meredith Gregory Newsgroups: gmane.science.mathematics.categories Subject: Conway Games over arbitrary (strong) monad? Date: Tue, 24 May 2011 00:21:17 -0700 Message-ID: Reply-To: Meredith Gregory NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1306268365 16278 80.91.229.12 (24 May 2011 20:19:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 24 May 2011 20:19:25 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Tue May 24 22:19:21 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QOy4V-0004HQ-IO for gsmc-categories@m.gmane.org; Tue, 24 May 2011 22:19:19 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:53529) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QOy1y-0001tD-GQ; Tue, 24 May 2011 17:16:42 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QOy1w-0007Qr-0O for categories-list@mlist.mta.ca; Tue, 24 May 2011 17:16:40 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6686 Archived-At: Dear Categorically Inclined, Has anyone transported the Conway Game construction to the categorical setting in such a way that it works over an arbitrary (strong) monad? If so, is there a reference? i've been experimenting with such a beast using the following recipe: 1. poke a hole in the Conway construction making it parametrically polymorphic in an 'atom' type (following an analogy with the relationship between ZF Set Theory and Fraenkl-Mostowski Set Theory) 2. use the monad to 'collect' the left and right components resulting in a domain eqn CG[M,A] = M[CG[M,A] + A] x M[CG[M,A] + A] For this to work out well enough to support the definitions of the field operations there have to be a few extra maps lying around and some coherence conditions on them. Maybe there's a simpler way to wire up this machine. If so, i'd love a reference. Or, maybe there's a flaw in approach, in which case i'd love to be enlightened. Best wishes, --greg -- L.G. Meredith Managing Partner Biosimilarity LLC 7329 39th Ave SW Seattle, WA 98136 +1 206.650.3740 http://biosimilarity.blogspot.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]