Separable extensions preserve finiteness of global dimension, Gorensteinness and regularity in compactly generated triangulated categories while relating their singularity categories up to retracts.
$\infty$-categorical group quotients via skew group algebras
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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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Homological Aspects of Separable Extensions of Triangulated Categories
Separable extensions preserve finiteness of global dimension, Gorensteinness and regularity in compactly generated triangulated categories while relating their singularity categories up to retracts.