Cofrobenius Corings and adjoint Functors

Details Cofrobenius Corings and adjoint Functors Cofrobenius Corings and adjoint Functors

2006-10-27

arxiv.org/abs/math/0610853v2

Mathematics

Rings and Algebras

Strongly revised version: major changes in section 3, 5.2 and 5.3, minor changes elsewhere. Change of title (on request of the

Scientific paper

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

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