Galois theory for comatrix corings: descent theory, Morita theory, Frobenius and separability properties

introduced comatrix corings, generalizing Sweedler’s canonical coring, and proved a new version of the Faith-fully Flat Descent Theorem. They also introduced Galois corings, as corings isomorphic to a comatrix coring. In this paper, we further investigate this theory. We prove a new version of the Joyal-Tierney Descent Theorem, and generalize the Galois Coring Structure Theorem. We associate a Morita con-text to a coring with a fixed comodule, and relate it to Galois-type properties of the coring. An affineness criterion is proved in the situation where the cor-ing is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius