Twisted separability for adjoint functors

Julien Bichon

Twisted separable functors generalize the separable functors of Nastasescu, Van den Bergh and Van Oystaeyen, and provide a convenient tool to compare various projective dimensions. We discuss when an adjoint functor is twisted separable, obtaining a version of Rafael's Theorem in the twisted case. As an application, we show that if R is Hopf-Galois object over a Hopf algebra A, then their Hochschild cohomological dimension coincide, provided that the cohomological dimension of A is finite and that R has a unital twisted trace with respect to a semi-colinear automorphism.

Keywords: Twisted separable adjoint functor, Hopf-Galois object, projective dimension

2020 MSC: 16T05, 16E10, 18G20, 18A40

Theory and Applications of Categories, Vol. 41, 2024, No. 5, pp 150-167.

Published 2024-03-05.

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