%0 Journal Article %T Equivalences between categories of modules and categories of comodules %A Joost Vercruysse %J Mathematics %D 2006 %I arXiv %X We show the close connection between appearingly different Galois theories for comodules introduced recently in [J. G\'omez-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. %U http://arxiv.org/abs/math/0604423v2