Geodesic
Genuine versus naïve symmetric monoidal $G$-categories
Documenta mathematica, Tome 28 (2023) no. 5, pp. 1079-1161

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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].
DOI : 10.4171/dm/933
Classification : 55P91, 55P48, 19D23, 55U35
Mots-clés : Genuine symmetric monoidal G-categories, operads, parsummable categories, equivariant infinite loop spaces, G-global homotopy theory, equivariant algebraic K-theory 
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     author = {Tobias Lenz},
     title = {Genuine versus na{\"\i}ve symmetric monoidal $G$-categories},
     journal = {Documenta mathematica},
     pages = {1079--1161},
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     year = {2023},
     doi = {10.4171/dm/933},
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Tobias Lenz. Genuine versus naïve symmetric monoidal $G$-categories. Documenta mathematica, Tome 28 (2023) no. 5, pp. 1079-1161. doi: 10.4171/dm/933

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