From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6032 Path: news.gmane.org!not-for-mail From: Paul Levy Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Tue, 3 Aug 2010 12:03:28 +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 1280917005 23182 80.91.229.12 (4 Aug 2010 10:16:45 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 4 Aug 2010 10:16:45 +0000 (UTC) Cc: Categories mailing list To: Richard Garner Original-X-From: majordomo@mlist.mta.ca Wed Aug 04 12:16:41 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 1Ogb1c-0001jr-US for gsmc-categories@m.gmane.org; Wed, 04 Aug 2010 12:16:41 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44880) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Ogazl-0007VJ-MC; Wed, 04 Aug 2010 07:14:45 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Ogaze-0007Aa-Ol for categories-list@mlist.mta.ca; Wed, 04 Aug 2010 07:14:39 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6032 Archived-At: 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"Combining effects: sum and tensor" by Hyland, Plotkin and Power: page 4, paragraph beginning "There is also relevant unpublished work by Paul Levy".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. 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/ ]