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Twisted separability for adjoint functors
Theory and applications of categories, Tome 41 (2024), pp. 150-167 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 16T05, 16E10, 18G20, 18A40
Keywords: Twisted separable adjoint functor, Hopf-Galois object, projective dimension 
@article{TAC_2024_41_a4,
     author = {Julien Bichon},
     title = {Twisted separability for adjoint functors},
     journal = {Theory and applications of categories},
     pages = {150--167},
     year = {2024},
     volume = {41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a4/}
}
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Julien Bichon. Twisted separability for adjoint functors. Theory and applications of categories, Tome 41 (2024), pp. 150-167. http://geodesic.mathdoc.fr/item/TAC_2024_41_a4/