Maps of monads - references

[Steven R. Costenoble <Steven.R.Costenoble@Hofstra.edu>]

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