From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: Sergey Goncharov <sergey@informatik.uni-bremen.de>
Cc: Categories mailing list <categories@mta.ca>
Subject: Re: Tensor of monads
Date: Fri, 30 Jul 2010 11:37:19 +0100 (BST) [thread overview]
Message-ID: <E1Oey01-0000dm-E4@mlist.mta.ca> (raw)
In-Reply-To: <4C5224A4.4000105@informatik.uni-bremen.de>
On Fri, 30 Jul 2010, Sergey Goncharov wrote:
> On 07/29/2010 03:24 PM, Prof. Peter Johnstone wrote:
>> Sorry, the previous posting was nonsense -- a bisemilattice is the
>> same thing as a semilattice, by the Eckmann-Hilton argument.
>> However, if you leave out the zero, and consider the "set of
>> nonempty subsets" monad, this time on the category of sets of
>> cardinality 2^n - 1 for some n, you do get a counterexample.
> This looks fine! 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?
>
Yes, it was: the fact that the unit for each semilattice structure is
a homomorphism for the other forces them to be the same.
Peter Johnstone
P.S. -- You can enlarge the base category to contain all finite sets
of odd cardinality (so that, for example, it's cartesian closed).
The free bi-(semilattice-without-unit) on three generators has 20
elements.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-07-30 10:37 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 ` Prof. Peter Johnstone [this message]
2010-07-30 22:41 ` Tensor of monads 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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