From: Toby Bartels <toby+categories@ugcs.caltech.edu>
To: categories@mta.ca
Subject: Eckmann-Hilton (Was: Tensor of monads)
Date: Sat, 31 Jul 2010 13:34:26 -0700 [thread overview]
Message-ID: <E1OfK3k-00021Z-9p@mlist.mta.ca> (raw)
In-Reply-To: <E1OexyK-0000Yh-0I@mlist.mta.ca>
Sergey Goncharov wrote in part:
>But I guess, Eckmann-Hilton argument does not apply to
>your previous example because it presupposes that the monoidal
>structures share the unit, which was not the case there, was it?
Actually, the requirements for Eckmann-Hilton are surprsingly weak!
As long as you have two binary operations on a given set,
each with its own unit, where one is a homomorphism WRT the other,
then everything else (associativity, same unit, etc) follows.
See http://ncatlab.org/nlab/show/Eckmann-Hilton+argument for details.
--Toby
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-07-31 20:34 UTC|newest]
Thread overview: 24+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-07-28 14:02 Tensor of monads 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 ` Toby Bartels [this message]
[not found] ` <4C5224A4.4000105@informatik.uni-bremen.de>
2010-07-30 10:37 ` 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
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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