Defining morphisms between monads in a 2-category C (where C = Cat if you like) the way I do in "The formal thy of mnds", I obtain a 2-category Mnd(C) of monads in C such that the inclusion C --> Mnd(C) has the Eilenberg-Moore construction as its right adjoint. On page 159 of the paper, J"urgen will find the 2-cell which satisfies his intuition; these are good for Kleisli's construction. Of course, we now know that the EM-construction is just a weighted (or "indexed") limit in the Cat-enriched context ("Limits indexed by cat-valued 2-functors" JPAA 1976?). Kleisli-construction is a weighted colimit. Also see SLNM 420 (Kelly-Street paper and "Elem cosmoi" Section 6 pp166-168). Regards, Ross =========================================================================