  Generalising the notion of Galois corings, Galois comodules were introduced
as comodules $P$ over an $A$-coring $\cC$ for which $P_A$ is finitely generated
and projective and the evaluation map $\mu_\cC:\Hom^\cC(P,\cC)\ot_SP\to \cC$ is
an isomorphism (of corings) where $S=\End^\cC(P)$. It was observed that for
such comodules the functors $\Hom_A(P,-)\ot_SP$ and $-\ot_A\cC$ from the
category of right $A$-modules to the category of right $\cC$-comodules are
isomorphic. In this note we call modules $P$ with this property {\em Galois
comodules} without requiring $P_A$ to be finitely generated and projective.
This generalises the old notion with this name but we show that essential
properties and relationships are maintained. These comodules are close to being
generators and have some common properties with tilting (co)modules. Some of
our results also apply to generalised Hopf Galois (coalgebra Galois)
extensions.
