From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6011 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Tensor of monads Date: Thu, 29 Jul 2010 23:44:13 -0400 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1280528728 19723 80.91.229.12 (30 Jul 2010 22:25:28 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Jul 2010 22:25:28 +0000 (UTC) To: "Sergey Goncharov" , Original-X-From: majordomo@mlist.mta.ca Sat Jul 31 00:25:27 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Oey19-00076W-Ft for gsmc-categories@m.gmane.org; Sat, 31 Jul 2010 00:25:27 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51744) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OexzT-0002bK-8g; Fri, 30 Jul 2010 19:23:43 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OexzO-0000bf-Pr for categories-list@mlist.mta.ca; Fri, 30 Jul 2010 19:23:39 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6011 Archived-At: Dear Sergey, Here is a simple example, based on the ordered class ORD of all ordinals numbers. The subclass LIMIT of all limit ordinals=20 is reflexive in ORD. Let us denote by L the resulting reflection = operator. Similarly, the subclass SUCC of all successor ordinals is reflexive in = ORD. Let us denote by S the resulting reflection operator.=20 The operators L and S cannot be bounded simultaneously by a reflection operator (=3D monad) since the classes LIMIT and SUCC have an empty intersection. Best, Andre -------- Message d'origine-------- De: Sergey Goncharov [mailto:sergey@informatik.uni-bremen.de] Date: mer. 28/07/2010 10:02 =C0: categories@mta.ca Objet : categories: Tensor of monads =20 Dear categorists, in "Combining algebraic e?ects with continuations", by Hyland et al. the = authors say carefully: "In general, the tensor product of two arbitrary=20 monads seems not to exist.." without providing a counterexample though,=20 presumably because they did not have any. Was there any progress=20 reported on this issue since then? Or maybe someone can even make up a=20 counterexample right on the nail? Thanks, --=20 Sergey Goncharov, Junior Researcher DFKI Bremen Phone: +49-421-218-64276 Safe and Secure Cognitive Systems Fax: +49-421-218-9864276 Cartesium, Enrique-Schmidt-Str. 5 Email: Sergey.Goncharov@dfki.de D-28359 Bremen Site: www.dfki.de/sks/staff/sergey [For admin and other information see: http://www.mta.ca/~cat-dist/ ]