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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.
Bayındır, Haldun Özgür 1 ; Chorny, Boris 2
@article{10_2140_agt_2023_23_43,
author = {Bay{\i}nd{\i}r, Haldun \"Ozg\"ur and Chorny, Boris},
title = {Admissible replacements for simplicial monoidal model categories},
journal = {Algebraic and Geometric Topology},
pages = {43--73},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {2023},
doi = {10.2140/agt.2023.23.43},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.43/}
}
TY - JOUR AU - Bayındır, Haldun Özgür AU - Chorny, Boris TI - Admissible replacements for simplicial monoidal model categories JO - Algebraic and Geometric Topology PY - 2023 SP - 43 EP - 73 VL - 23 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.43/ DO - 10.2140/agt.2023.23.43 ID - 10_2140_agt_2023_23_43 ER -
%0 Journal Article %A Bayındır, Haldun Özgür %A Chorny, Boris %T Admissible replacements for simplicial monoidal model categories %J Algebraic and Geometric Topology %D 2023 %P 43-73 %V 23 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.43/ %R 10.2140/agt.2023.23.43 %F 10_2140_agt_2023_23_43
Bayındır, Haldun Özgür; Chorny, Boris. Admissible replacements for simplicial monoidal model categories. Algebraic and Geometric Topology, Tome 23 (2023) no. 1, pp. 43-73. doi: 10.2140/agt.2023.23.43
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