An adjoint pair of contravariant functors between abelian categories can be
extended to the adjoint pair of their derived functors in the associated
derived categories. We describe the reflexive complexes and interpret the
achieved results in terms of objects of the initial abelian categories. In
particular we prove that, for functors of any finite cohomological dimension,
the objects of the initial abelian categories which are reflexive as stalk
complexes form the largest class where a Cotilting Theorem in the sense of
Colby and Fuller works
