From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6010 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Fri, 30 Jul 2010 11:37:19 +0100 (BST) Message-ID: References: <4C5224A4.4000105@informatik.uni-bremen.de> Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1280528725 19715 80.91.229.12 (30 Jul 2010 22:25:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 30 Jul 2010 22:25:25 +0000 (UTC) Cc: Categories mailing list To: Sergey Goncharov Original-X-From: majordomo@mlist.mta.ca Sat Jul 31 00:25:24 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Oey15-000742-JW for gsmc-categories@m.gmane.org; Sat, 31 Jul 2010 00:25:23 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51766) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Oey06-0002fx-08; Fri, 30 Jul 2010 19:24:21 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Oey01-0000dm-E4 for categories-list@mlist.mta.ca; Fri, 30 Jul 2010 19:24:17 -0300 In-Reply-To: <4C5224A4.4000105@informatik.uni-bremen.de> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6010 Archived-At: 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/ ]