2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58928We study when induction functors (and their adjoints) between categories of Doi-Hopf modules and, more generally, entwined modules are separable, resp. Frobenius. We present a unified approach, leading to new proofs of old results by the authors, as well as to some new ones. Also our methods provide a categorical explanation for the relationship between separability and Frobenius properties.28 pages, LaTeX; Contribution to the proceedings of the ``Fifth week on algebra and geometry (SAGA5)'', Leon, Spain 1999Rings and AlgebrasQuantum Algebra16W30, 16S40text