From: Paul Levy <pbl@cs.bham.ac.uk>
To: Richard Garner <r.h.g.garner@gmail.com>
Cc: Categories mailing list <categories@mta.ca>
Subject: Re: Tensor of monads
Date: Tue, 3 Aug 2010 12:03:28 +0100 [thread overview]
Message-ID: <E1Ogaze-0007Aa-Ol@mlist.mta.ca> (raw)
In-Reply-To: <AANLkTimd202AX=3hUqU9ABkKUy9Z4Loh1RXTiDgVZ3Ku@mail.gmail.com>
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paragraph beginning "There is also relevant unpublished work by Paul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/ ]
next prev parent reply other threads:[~2010-08-03 11:03 UTC|newest]
Thread overview: 24+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-07-28 14:02 Sergey Goncharov
2010-07-29 8:21 ` N.Bowler
2010-07-29 9:18 ` Prof. Peter Johnstone
2010-07-29 10:29 ` Michael Barr
2010-07-31 8:45 ` Richard Garner
[not found] ` <AANLkTinxyVQ1fXu7DLWu4CUF3AP2KPX6PLQFDB+zG4Ef@mail.gmail.com>
2010-07-31 12:48 ` Michael Barr
[not found] ` <alpine.LRH.2.00.1007291006210.5174@siskin.dpmms.cam.ac.uk>
2010-07-29 13:24 ` Prof. Peter Johnstone
[not found] ` <alpine.LRH.2.00.1007291422370.5174@siskin.dpmms.cam.ac.uk>
2010-07-30 1:02 ` Sergey Goncharov
2010-07-31 20:34 ` Eckmann-Hilton (Was: Tensor of monads) Toby Bartels
[not found] ` <4C5224A4.4000105@informatik.uni-bremen.de>
2010-07-30 10:37 ` Tensor of monads Prof. Peter Johnstone
2010-07-30 22:41 ` Tom Leinster
2010-08-01 19:49 ` Ronnie Brown
2010-08-02 9:47 ` Ronnie Brown
2010-08-01 0:31 ` Richard Garner
2010-08-02 19:55 ` Paul Levy
2010-08-03 6:39 ` Richard Garner
[not found] ` <AANLkTimd202AX=3hUqU9ABkKUy9Z4Loh1RXTiDgVZ3Ku@mail.gmail.com>
2010-08-03 11:03 ` Paul Levy [this message]
2010-08-09 20:26 ` Paul Levy
2010-08-05 20:06 ` Sergey Goncharov
2010-08-08 19:24 ` Gordon Plotkin
2010-07-30 3:44 ` Joyal, André
[not found] ` <AANLkTin5+paq8sP-eVjdf8rZOyA-z=t6QzAhCqVUsyQi@mail.gmail.com>
2010-08-01 9:13 ` Richard Garner
2010-08-02 14:17 ` Prof. Peter Johnstone
[not found] ` <alpine.LRH.2.00.1008021514290.18118@siskin.dpmms.cam.ac.uk>
2010-08-02 21:12 ` Richard Garner
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