Re: Tensor of monads

[Richard Garner <r.h.g.garner@gmail.com>]

Isn't P * P isomorphic to P, by the Eckmann-Hilton argument?

On 29 July 2010 20:29, Michael Barr <barr@math.mcgill.ca> wrote:

> There are examples in Ernie Manes's 1967 thesis.  Perhaps the simplest
> (although it piggybacks on the non-existence of free complete boolean
> algebras that had been know for only a few years at the time) is that the
> tensor product of the complete sup semilattice triple with itself doesn't
> exist.  The triple takes a set X to 2^X and can be interpreted also as the
> complete inf semilattice triple.  On the other hand, I think Manes showed
> that the tensor product of the beta triple with itself exists, but is one
> of the two inconsistent triples, the one that fixes the empty set and
> takes all non-empty sets to one point.  (The other inconsistent triple
> takes all sets to one point.)
>
>
> On Wed, 28 Jul 2010, Sergey Goncharov wrote:
>
>  Dear categorists,
>>
>> in "Combining algebraic eects with continuations", by Hyland et al. the
>>
>> authors say carefully: "In general, the tensor product of two arbitrary
>> monads seems not to exist.." without providing a counterexample though,
>> presumably because they did not have any. Was there any progress reported
>> on
>> this issue since then? Or maybe someone can even make up a counterexample
>> right on the nail?
>>
>> Thanks,
>>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]