From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6007 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Thu, 29 Jul 2010 06:29:42 -0400 (EDT) Message-ID: References: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1280449749 5281 80.91.229.12 (30 Jul 2010 00:29:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Jul 2010 00:29:09 +0000 (UTC) Cc: categories@mta.ca To: Sergey Goncharov Original-X-From: majordomo@mlist.mta.ca Fri Jul 30 02:29:08 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OedTH-000279-JZ for gsmc-categories@m.gmane.org; Fri, 30 Jul 2010 02:29:07 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46748) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OedO7-0004CK-F4; Thu, 29 Jul 2010 21:23:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OedO1-00037l-E2 for categories-list@mlist.mta.ca; Thu, 29 Jul 2010 21:23:41 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6007 Archived-At: 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/ ]