Hom-corings, Hom-coalgebra Galois Extensions and Partial Coactions of Monoidal Hom-Hopf Algebras

In this paper, we give the notion of (lax or weak) Hom-corings, which leads to the introduction of partial coaction of a Hom-Hopf algebra on a Hom-algebra. We construct several pairs of adjoint functors, and define Galois Hom-corings, as a special case of which Galois Hom-coalgebras are introduced.