Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories

Abstract

We prove the theorem stated in the title. More precisely, we show the stronger statement that every symmetric monoidal left adjoint functor between presentably symmetric monoidal infinity-categories is represented by a strong symmetric monoidal left Quillen functor between simplicial, combinatorial and left proper symmetric monoidal model categories.

v3: 17 pages, references updated and exposition improved, accepted for publication in Algebraic and Geometric Topology