Twisted separability for adjoint functors
Category Theory
2023-07-13 v1 Quantum Algebra
Abstract
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 is Hopf-Galois object over a Hopf algebra , then their Hochschild cohomological dimension coincide, provided that the cohomological dimension of is finite and that has a unital twisted trace with respect to a semi-colinear automorphism.
Cite
@article{arxiv.2307.05980,
title = {Twisted separability for adjoint functors},
author = {Julien Bichon},
journal= {arXiv preprint arXiv:2307.05980},
year = {2023}
}