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?
Thanks a lot, -- Sergey Goncharov, Junior Researcher DFKI Bremen Phone: +49-421-218-64276 Safe and Secure Cognitive Systems Fax: +49-421-218-9864276 Cartesium, Enrique-Schmidt-Str. 5 Email: Sergey.Goncharov@dfki.de D-28359 Bremen Site: www.dfki.de/sks/staff/sergey ------------------------------------------------------------- Deutsches Forschungszentrum fuer Kuenstliche Intelligenz GmbH Firmensitz: Trippstadter Strasse 122, D-67663 Kaiserslautern Geschaeftsfuehrung: Prof. Dr. Dr. h.c. mult. Wolfgang Wahlster (Vorsitzender) Dr. Walter Olthoff Vorsitzender des Aufsichtsrats: Prof. Dr. h.c. Hans A. Aukes Amtsgericht Kaiserslautern, HRB 2313 ------------------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]