Genuine versus naïve symmetric monoidal G-categories

Lenz, Tobias

doi:10.4171/DM/933

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Genuine versus naïve symmetric monoidal G-categories

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Lenz, Tobias
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2203.02277
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https://doi.org/10.4171/dm/933
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Lenz, T. (2023). Genuine versus naïve symmetric monoidal G-categories. Documenta Mathematica, 28(5), 1079-1161. doi:10.4171/DM/933.

Cite as: https://hdl.handle.net/21.11116/0000-000E-0CD6-4

Abstract

We prove that through the eyes of equivariant weak equivalences the genuine symmetric monoidal G-categories of Guillou and May [Algebr. Geom. Topol. 17 (2017), no. 6, 3259–3339] are equivalent to just ordinary symmetric monoidal categories with G-action. Along the way, we give an operadic model of global infinite loop spaces and provide an equivalence between the equivariant category theory of genuine symmetric monoidal G-categories and the G-parsummable categories studied by Schwede [J. Topol. 15 (2022), no. 3, 1325–1454] and the author [New York J. Math. 29 (2023), 635–686].