We contribute to the formal theory of pseudomonads, i.e. the analogue for
pseudomonads of the formal theory of monads. In particular, we solve a problem
posed by Steve Lack by proving that, for every Gray-category K, there is a
Gray-category Psm(K) of pseudomonads, pseudomonad morphisms, pseudomonad
transformations and pseudomonad modifications in K. We then establish a
triequivalence between Psm(K) and the Gray-category of pseudomonads introduced
by Marmolejo. Finally, these results are applied to give a clear account of the
coherence conditions for pseudodistributive laws. 40 pages. Comments welcome.Comment: This submission replaces arXiv:0907:1359v1, titled "On the coherence
conditions for pseudo-distributive laws". 40 page