Combinatorial model categories are equivalent to presentable quasicategories

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.

35 pages. Comments and questions are welcome. v2: Minor corrections and improvements. v3: Identical to the journal version except for formatting and style

References in corpus (7)

• Higher Topos Theory
• Sheafifiable homotopy model categories
• Simplicial structures on model categories and functors
• Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories
• Quillen adjunctions induce adjunctions of quasicategories
• Rectification of enriched infinity-categories
• On the $\infty$-categorical Whitehead theorem and the embedding of quasicategories in prederivators