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Presentably symmetric monoidal $\infty$–categories are represented by symmetric monoidal model categories

Thomas Nikolaus and Steffen Sagave
Algebraic & Geometric Topology 17 (2017) 3189–3212
DOI: 10.2140/agt.2017.17.3189
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 ∞-categories is represented by a strong symmetric monoidal left Quillen functor between simplicial, combinatorial and left proper symmetric monoidal model categories.

Keywords
infinity-category, quasicategory, symmetric monoidal model category
Mathematical Subject Classification 2010
Primary: 55U35
Secondary: 18D10, 18G55
References
Publication
Received: 31 January 2017
Accepted: 8 March 2017
Published: 19 September 2017
Authors
Thomas Nikolaus
Max Planck Institut für Mathematik
Bonn
Germany
http://people.mpim-bonn.mpg.de/thoni/
Steffen Sagave
IMAPP
Radboud University Nijmegen
Nijmegen
The Netherlands
http://www.math.ru.nl/~sagave/