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Co-Frobenius corings and adjoint functors
Journal article   Open access   Peer reviewed

Co-Frobenius corings and adjoint functors

M. C Iovanov and J Vercruysse
Journal of pure and applied algebra, Vol.212(9), pp.2027-2058
09/01/2008
DOI: 10.1016/j.jpaa.2007.11.015
url
https://doi.org/10.1016/j.jpaa.2007.11.015View
Published (Version of record) Open Access

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-Froben ius 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-coFrobenius 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. (c) 2008 Elsevier B. V. All rights reserved.
Mathematics Mathematics, Applied Physical Sciences Science & Technology

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