We investigate functors between abelian categories having a left adjoint and a right adjoint that are \emph{ similar} (these functors are called \emph{ quasi-Frobenius functors}). We introduce the notion of a \emph{ quasi-Frobenius bimodule} and give a characterization of these bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of quasi-Frobenius homomorphism of corings is introduced. Finally, a version of the endomorphism ring Theorem for quasi-Frobenius extensions in terms of corings is obtained.
Categories: math.RA