Admissible replacements for simplicial monoidal model categories

Bayındır, Haldun Özgür; Chorny, Boris

doi:10.2140/agt.2023.23.43

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Admissible replacements for simplicial monoidal model categories

Haldun Özgür Bayındır and Boris Chorny

Algebraic & Geometric Topology 23 (2023) 43–73

DOI: 10.2140/agt.2023.23.43

Abstract

Using Dugger’s construction of universal model categories, we produce replacements for simplicial and combinatorial symmetric monoidal model categories with better operadic properties. Namely, these replacements admit a model structure on algebras over any given colored operad.

As an application, we show that in the stable case, such symmetric monoidal model categories are classified by commutative ring spectra when the monoidal unit is a compact generator. In other words, they are strong monoidally Quillen equivalent to modules over a uniquely determined commutative ring spectrum.

Keywords

symmetric monoidal model category, operad

Mathematical Subject Classification

Primary: 18M05, 55P99

References

Publication

Received: 25 August 2020

Revised: 9 September 2021

Accepted: 14 October 2021

Published: 27 March 2023

Authors

Haldun Özgür Bayındır
Department of Mathematics City, University of London London United Kingdom

Boris Chorny
Department of Mathematics, Physics and Computer Science University of Haifa at Oranim Tivon Israel

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Volume 23, issue 1 (2023)