Presentably symmetric monoidal ∞–categories are represented by symmetric monoidal model categories

Nikolaus, Thomas; Sagave, Steffen

doi:10.2140/agt.2017.17.3189

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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 $\infty$ -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

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/

Volume 17, issue 5 (2017)