From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6013 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Sat, 31 Jul 2010 18:45:14 +1000 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1280613427 2124 80.91.229.12 (31 Jul 2010 21:57:07 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 31 Jul 2010 21:57:07 +0000 (UTC) Cc: Sergey Goncharov , categories@mta.ca To: Michael Barr Original-X-From: majordomo@mlist.mta.ca Sat Jul 31 23:57:04 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 1OfK3D-0002OO-3z for gsmc-categories@m.gmane.org; Sat, 31 Jul 2010 23:57:03 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46578) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OfK2G-0002H7-Pp; Sat, 31 Jul 2010 18:56:04 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OfK2B-0001y6-0Z for categories-list@mlist.mta.ca; Sat, 31 Jul 2010 18:55:59 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6013 Archived-At: Isn't P * P isomorphic to P, by the Eckmann-Hilton argument? On 29 July 2010 20:29, Michael Barr wrote: > There are examples in Ernie Manes's 1967 thesis. Perhaps the simplest > (although it piggybacks on the non-existence of free complete boolean > algebras that had been know for only a few years at the time) is that the > tensor product of the complete sup semilattice triple with itself doesn't > exist. The triple takes a set X to 2^X and can be interpreted also as the > complete inf semilattice triple. On the other hand, I think Manes showed > that the tensor product of the beta triple with itself exists, but is one > of the two inconsistent triples, the one that fixes the empty set and > takes all non-empty sets to one point. (The other inconsistent triple > takes all sets to one point.) > > > On Wed, 28 Jul 2010, Sergey Goncharov wrote: > > Dear categorists, >> >> in "Combining algebraic eects with continuations", by Hyland et al. the >> >> authors say carefully: "In general, the tensor product of two arbitrary >> monads seems not to exist.." without providing a counterexample though, >> presumably because they did not have any. Was there any progress reported >> on >> this issue since then? Or maybe someone can even make up a counterexample >> right on the nail? >> >> Thanks, >> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]