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arXiv · 2501.13666

$\infty$-categorical group quotients via skew group algebras

Merlin Christ
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Abstract

We relate group quotients of dg-categories and linear stable $\infty$-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also treat the cases of group actions on dg-categories, with corresponding skew group dg-categories, and of orbit dg-categories. Finally, we describe a version of the skew group algebra in the setting of ring spectra and relate it with $\infty$-categorical group quotients.

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Merlin Christ. 2025-01-23. $\infty$-categorical group quotients via skew group algebras. https://arxiv.org/abs/2501.13666

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