Dear People,
Dear David,
... I'm considering a "category" whose objects are type constructors, given as endofunctions on a base category, and whose arrows are _situated monads_ relating the type constructors. ...
To me this gives your question an entirely different flavor. You
Whoops. I had meant that to be private. I guess I may as well add a few more references in public mode. triples: E. Manes, Algebraic Theories, 1976, Springer-Verlag the monoidal case of bicategories: A. Joyal and R. Street, The geometry of tensor calculus, I, 1991, Advances in Mathematics some implicit but usually unmentioned coherence trickery: G. Kelly, On MacLane's condition of coherence of natural associativities, commutativities, etc., 1964, J. Algebra Oh well, Jim