Co-Frobenius corings and adjoint functors |
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Authors: | MC Iovanov J Vercruysse |
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Affiliation: | a Faculty of Mathematics and Informatics, University of Bucharest, Str. Academiei 14, RO-010014, Bucharest 1, Romania b State University of New York - Buffalo, 244 Mathematics Building, Buffalo NY, 14260-2900, USA c Faculty of Engineering, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussel, Belgium |
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Abstract: | 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. |
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Keywords: | 16W30 |
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