  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; arXiv:1809.03017] 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; arXiv:1912.08872] and the author [New York J.
Math. 29 (2023), 635-686; arXiv:2009.07004].
