Re: Tensor of monads

[Michael Barr <barr@math.mcgill.ca>]

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/ ]