Lifting Enhanced Factorization Systems to Functor $2$-Categories

Abstract

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.

19 pages. References reordered, corrected some typographical errors, and removed redundancy from the proof of Lem. 3.1. See author's website for a version of the paper with working hyperlinks