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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


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  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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