Re: Maps of monads - references

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

Thanks, all, for the many replies (private as well as to the list).
Among other interesting references, almost everyone suggested Ross
Street's "The formal theory of monads" as well as the recent followup
by Street and Steve Lack, "The formal theory of monads II." I'll add
those to my summer reading list.

--Steve Costenoble


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
>
>
>