L-2-von Neumann modules, their Relative Tensor Products and the spatial derivative

We develop a theory of L-2-von Neumann modules, which encompasses a reformu lation of Connes' Spatial Derivative, and the Relative Tensor Product of Sa uvageot. We demonstrate the naturality of the relative tensor product const ruction in the category of L-2-von Neumann bimodules. Finally, we give evid ence for the claim that the relative tensor product is essentially the only tensor product which should be used when considering this tensor category.