Re: Maps of monads - references

[Prof. Dr. Pumpluen <dieter.pumpluen@FernUni-Hagen.de>]

There is still another, very detailed reference (probably earlier) to this
topic in my paper "Eine Bemerkung ueber Monaden und adjungierte Funktoren",
Math. Ann.185, 329-337 (1970).

                  Best regards  Nico Pumpluen.

On Jul 10, 2007, at 9:25 AM, Steven R. Costenoble wrote:

> In Toposes, Triples, and Theories, Barr and Wells define a morphism
> of triples (which, being a student of Peter May, I will call a map of
> monads) in the context of two monads on a given category C. I have a
> situation where I have two categories C and D, a monad S on C, a
> monad T on D, and a functor F: C -> D. There is a fairly obvious
> generalization of the TTT definition, to say that a map from S to T
> is a natural transformation FS -> TF making certain diagrams commute.
> My guess is that someone else noticed this long ago, so I'm looking
> for references to where this has appeared in the literature. I'm
> particularly interested in references that include the fact (at
> least, I'm pretty sure it's a fact) that such maps are in one-to-one
> correspondence with extensions of F to a functor between the
> respective Kleisli categories of S and T.
>
> Thanks in advance.
>
> --Steve Costenoble
>
>
>