  We study 2-monads and their algebras using a Cat-enriched version of Quillen
model categories, emphasizing the parallels between the homotopical and
2-categorical points of view. Every 2-category with finite limits and colimits
has a canonical model structure in which the weak equivalences are the
equivalences; we use these to construct more interesting model structures on
2-categories, including a model structure on the 2-category of algebras for a
2-monad T, and a model structure on a 2-category of 2-monads on a fixed
2-category K.
