Homotopy-theoretic aspects of 2-monads

Stephen Lack

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.

Journal of Homotopy and Related Structures, Vol. 2(2007), No. 2, pp. 229-260