Summary: The category of von Neumann correspondences from \({\mathcal B}\) to \({\mathcal C}\) (or von Neumann \({\mathcal B}\)-\({\mathcal C}\)-modules) is dual to the category of von Neumann correspondences from \({\mathcal C}'\) to \({\mathcal B}'\) 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.
For the entire collection see [Zbl 1101.81002].