Genuine vs. na\"ive symmetric monoidal G-categories
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; arXiv:1809.03017] 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; arXiv:1912.08872] and the author [New York J. Math. 29 (2023), 635-686; arXiv:2009.07004].
Keywords
Cite
@article{arxiv.2203.02277,
title = {Genuine vs. na\"ive symmetric monoidal G-categories},
author = {Tobias Lenz},
journal= {arXiv preprint arXiv:2203.02277},
year = {2024}
}
Comments
Final version, based on feedback by referees: improved exposition, added subsection 2.4, generalized construction in Section 5, various minor corrections. 80 pages