  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.

Rings and Algebras;Quantum Algebra