Let R be the hyperfinite type III1 factor (if you don't know what that is, "let R be a ring" is a good enough approximation). The following category is equivalent to the category of R-R-bimodules on infinite dimensional separable Hilbert spaces.
Objects: Unital ring homomorphisms R → R.
Morphisms: Hom(φ,ψ) =
{x∈R : ∀y∈R, x φ(y) = ψ(y) x }
Composition of morphisms is given by multiplication in R. This category is actually a strict monoidal, with monoidal structure given by composition of ring homomorphisms.
