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

By Stefaan Caenepeel, Erwin de Groot, Joost Vercruysse. 2004

46 citations recorded by the source corpus.

El Kaoutit and Gomez Torrecillas 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca510e853a6a77a43d7eee8b417a722ee6219e79

Citations in the corpus

• Monads of effective descent type and comonadicity (2006, unknown): “This case is considered by L. El Kaoutit and J. Gómez Torrecillas in [16] and S. Caenepeel, E. De Groot and J. Vercruysse in [13].”