Accessible model categories

TL;DR

This paper establishes a characterization of accessible weak factorization systems in locally presentable categories and explores an analogy of Smith's theorem within accessible model categories.

Contribution

It provides a new equivalence criterion for accessible weak factorization systems and extends Smith's theorem analogy to accessible model categories.

Findings

Weak factorization systems are accessible iff small generated.

An analogy of Smith's theorem is developed for accessible model categories.

Provides a new perspective on the structure of accessible model categories.

Abstract

We prove that a weak factorization system on a locally presentable category is accessible if and only if it is small generated in the sense of R. Garner. Moreover, we discuss an analogy of Smith's theorem for accessible model categories.