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Admissible replacements for simplicial monoidal model categories

Haldun Özgür Bayındır and Boris Chorny

Algebraic & Geometric Topology 23 (2023) 43–73

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.

symmetric monoidal model category, operad
Mathematical Subject Classification
Primary: 18M05, 55P99
Received: 25 August 2020
Revised: 9 September 2021
Accepted: 14 October 2021
Published: 27 March 2023
Haldun Özgür Bayındır
Department of Mathematics
City, University of London
United Kingdom
Boris Chorny
Department of Mathematics, Physics and Computer Science
University of Haifa at Oranim

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