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Homotopy-theoretic aspects of 2-monads
#
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