Lifting Enhanced Factorization Systems to Functor $ 2 $-Categories

TL;DR

This paper establishes conditions under which enhanced factorization systems on a 2-category can be lifted to functor 2-categories, providing coherence results relevant to 2-monads and equivariant infinite loop space theory.

Contribution

It introduces sufficient conditions for lifting enhanced factorization systems to functor 2-categories, extending previous work and aiding coherence in 2-monad applications.

Findings

Provides coherence results for 2-monads on functor 2-categories.

Extends lifting techniques for factorization systems to 2-categories.

Supports ongoing research in equivariant infinite loop space theory.

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.