# Combinatorial homotopy categories

## TL;DR

This paper discusses the properties of homotopy categories derived from combinatorial model categories, emphasizing their well-generated nature and the applicability of Ohkawa's theorem.

## Contribution

It highlights the structural properties of homotopy categories of combinatorial model categories, extending understanding of their foundational features.

## Key findings

- Homotopy categories of combinatorial model categories are well generated.
- They satisfy a broad version of Ohkawa's theorem.
- These properties facilitate further mathematical analysis.

## Abstract

A model category is called combinatorial if it is cofibrantly generated and its underlying category is locally presentable. As shown in recent years, homotopy categories of combinatorial model categories share useful properties, such as being well generated and satisfying a very general form of Ohkawa's theorem.