Combinatorial model categories are equivalent to presentable quasicategories

TL;DR

This paper proves an equivalence between combinatorial model categories and presentable quasicategories, showing they are different models describing the same underlying (infinity,1)-category structures.

Contribution

It establishes a Dwyer-Kan equivalence linking combinatorial model categories and presentable quasicategories, unifying different frameworks for (infinity,1)-categories.

Findings

Combinatorial model categories are equivalent to presentable quasicategories.

Underlying quasicategories of these models are also equivalent.

Provides a unified understanding of models for (infinity,1)-categories.

Abstract

We establish a Dwyer-Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable (infinity,1)-categories. This implies that the underlying quasicategories of these relative categories are also equivalent.