In this paper we give sufficient conditions for lifting an enhanced factorization system $ (\mathcal{ E}, \mathcal{ M}) $ on a $ 2 $-category $ \mathbf{ D} $ to the functor $ 2 $-category $ \mathbf{ D}^{ \mathbf{ C}} $, where $ \mathbf{ C} $ is a small $ 2 $-category. Due to previous work of Lack, our work provides coherence results for $ 2 $-monads on functor $ 2 $-categories. These coherence results are of immediate interest to an ongoing collaboration of Guillou, May, Merling, and Osorno on equivariant infinite loop space theory.
Categories: math.CT