  The category of von Neumann correspondences from B to C (or von Neumann
B-C-modules) is dual to the category of von Neumann correspondences from C' to
B' via a functor that generalizes naturally the functor that sends a von
Neumann algebra to its commutant and back. We show that under this duality,
called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the
categories of representations of two von Neumann algebras) switches into
Blecher's Eilenberg-Watts theorem (on functors between the categories of von
Neumann modules over two von Neumann algebras) and back.
