Remarks on combinatorial and accessible model categories

TL;DR

This paper investigates properties of combinatorial and accessible model categories, providing new insights and examples, including a non-accessible weak factorization system on a locally presentable category.

Contribution

It presents new results on accessible functors and model categories, notably an example of a weak factorization system that is not accessible.

Findings

Established results about combinatorial and accessible model categories

Provided an example of a non-accessible weak factorization system

Analyzed properties of accessible functors using full images

Abstract

Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.