Genuine versus naïve symmetric monoidal -categories
Tobias Lenz
Universiteit Utrecht, Netherlands; Rheinische Friedrich-Wilhelms-Universität Bonn, Germany
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Abstract
We prove that through the eyes of equivariant weak equivalences the genuine symmetric monoidal -categories of Guillou and May [Algebr. Geom. Topol. 17 (2017), no. 6, 3259–3339] are equivalent to just ordinary symmetric monoidal categories with -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 -categories and the -parsummable categories studied by Schwede [J. Topol. 15 (2022), no. 3, 1325–1454] and the author [New York J. Math. 29 (2023), 635–686].
Cite this article
Tobias Lenz, Genuine versus naïve symmetric monoidal -categories. Doc. Math. 28 (2023), no. 5, pp. 1079–1161
DOI 10.4171/DM/933