  We prove a generalization of a theorem of Bunge and Gray about forming colax
adjunctions out of relative Kan extensions and apply it to the study of the
Kleisli 2-category for a lax-idempotent pseudomonad. For instance, we establish
the weak completeness of the Kleisli 2-category and describe colax
change-of-base adjunctions between Kleisli 2-categories. Our approach covers
such examples as the bicategory of small profunctors and the 2-category of lax
triangles in a 2-category. The duals of our results provide lax analogues of
classical results in two-dimensional monad theory: for instance, establishing
the weak cocompleteness of the 2-category of strict algebras and lax morphisms
and the existence of colax change-of-base adjunctions.
