As we know, a monad functor between two monads (possibly on different categories) can be lifted to a functor between the algebra categories. Fauser and I needed a corresponding 2-categorical result: a 2-monad 2-functor (of course, the natural transformation involved needs to be 2-natural) between two 2-monads (possibly on different 2-categories) can be lifted to a 2-functor between the lax algebra 2-categories. Also the lifting preserves pseudo-ness and strictness of the algebras. We checked all the equations and it works, but we're not experts on the 2-categorical literature and we wonder if it's already known. Our first literature searches haven't shown up anything - though even the 1-categorical case (which surely is well known) is elusive. Has anyone seen this result before? Steve Vickers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]