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

TL;DR

This paper proves that presentably symmetric monoidal infinity-categories can be modeled by symmetric monoidal model categories, establishing a strong correspondence between abstract infinity-category theory and concrete model category frameworks.

Contribution

It demonstrates that every symmetric monoidal left adjoint functor between presentably symmetric monoidal infinity-categories is represented by a strong symmetric monoidal left Quillen functor between suitable model categories.

Findings

Every symmetric monoidal left adjoint functor is represented by a Quillen functor.

The result applies to simplicial, combinatorial, and left proper model categories.

Establishes a concrete model for abstract symmetric monoidal infinity-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.