#### Volume 17, issue 5 (2017)

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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
##### 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 $\infty$-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
##### 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/