From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6038 Path: news.gmane.org!not-for-mail From: Paul Levy Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Mon, 9 Aug 2010 21:26:28 +0100 Message-ID: References: Reply-To: Paul Levy NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1281421823 25812 80.91.229.12 (10 Aug 2010 06:30:23 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 10 Aug 2010 06:30:23 +0000 (UTC) To: Richard Garner , Categories mailing list Original-X-From: majordomo@mlist.mta.ca Tue Aug 10 08:30:22 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 1OiiLt-0004Lj-8P for gsmc-categories@m.gmane.org; Tue, 10 Aug 2010 08:30:21 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:59278) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OiiKW-0006O8-7b; Tue, 10 Aug 2010 03:28:56 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OiiKI-0002PV-V2 for categories-list@mlist.mta.ca; Tue, 10 Aug 2010 03:28:43 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6038 Archived-At: On 3 Aug 2010, at 12:03, Paul Levy wrote: > > On 3 Aug 2010, at 07:39, Richard Garner wrote: > >> Dear Paul, >> >> Thanks for your perspicuous message. > > And thanks for your more perspicuous reply! Your argument apparently > applies to both coproduct and tensor of strong monads, and also to a > free strong monad on a strong endofunctor. Each of these can be > characterized both by a universal property and by a left adjoint to a > forgetful functor from an algebra category. Nice. > >> Your general definition of tensor product really cuts to the heart >> of the matter, and agrees with the cases where I knew how to take >> tensors previously. Has it been written down somewhere? It seems >> very natural. > > The universal property is alluded to in the TCS paper "Combining > effects: sum and tensor" by Hyland, Plotkin and Power: page 4, > paragraph beginning "There is also relevant unpublished work by Paul > Levy". I gave up on it (i.e. the universal property) thinking it was > too weak. Now you've shown me it wasn't. I should also have said that the universal property - though not the notion of "commuting S,T-algebra" in the form I stated it - did appear in the paper Combining algebraic effects with continuations, by Hyland, me, Plotkin and Power. Sorry for forgetting this, it's been a while. Also, the proof of Theorem 4 (and also that of Prop. 3) is similar to the one you provided, although the result is somewhat different. Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]