Abstract
We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gómez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 (2007), 271–306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 (2006), 2683–2711]. 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.
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