2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111625We show the close connection between appearingly different Galois theories for comodules introduced recently in [J. Gómez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, arXiv:math.RA/0509106.] and [R. Wisbauer, On Galois comodules (2004), to appear in Comm. Algebra.]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules.19 pages, some corrections and additions to version 1Rings and AlgebrasQuantum Algebra16W30text