Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties
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- by S. Caenepeel, E. De Groot and J. Vercruysse PDF
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Abstract:
El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler’s canonical coring, and proved a new version of the Faithfully 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 context 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 coring is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius.References
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Additional Information
- S. Caenepeel
- Affiliation: Faculty of Engineering, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
- Email: scaenepe@vub.ac.be
- E. De Groot
- Affiliation: Faculty of Engineering, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
- Email: edegroot@vub.ac.be
- J. Vercruysse
- Affiliation: Faculty of Engineering, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
- MR Author ID: 734258
- ORCID: 0000-0002-8154-5357
- Email: joost.vercruysse@vub.ac.be
- Received by editor(s): March 3, 2004
- Received by editor(s) in revised form: October 19, 2004
- Published electronically: July 21, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 185-226
- MSC (2000): Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9947-06-03857-8
- MathSciNet review: 2247888