Co-Frobenius corings and adjoint functors

• Autores: Miodrag Cristian Iovanov, J. Vercruysse
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 9, 2008, págs. 2027-2058
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.11.015
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• Resumen

  • We study co-Frobenius and more generally quasi-co-Frobenius corings over arbitrary base rings and over PF base rings in particular. We generalize some results about co-Frobenius and quasi-co-Frobenius coalgebras to the case of non-commutative base rings and give several new characterizations for co-Frobenius and more generally quasi-co-Frobenius corings, some of them are new even in the coalgebra situation. We construct Morita contexts to study Frobenius properties of corings and a second kind of Morita contexts to study adjoint pairs. Comparing both Morita contexts, we obtain our main result that characterizes quasi-co-Frobenius corings in terms of a pair of adjoint functors (F,G) such that (G,F) is locally quasi-adjoint in a sense defined in this note.