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

References in corpus (3)

• Higher Topos Theory
• Admissibility and rectification of colored symmetric operads
• Strictly commutative models for E-infinity quasi-categories

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• On rectification and enrichment of infinity properads
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• Homotopy invariance of convolution products
• Combinatorial model categories are equivalent to presentable quasicategories
• On the equivalence of AQFTs and prefactorization algebras
• Admissible replacements for simplicial monoidal model categories
• Monoidal Relative Categories Model Monoidal $\infty$-Categories
• $C^{\ast }$-categorical prefactorization algebras for superselection sectors and topological order