Realizations of rigid C-tensor categories as bimodules over GJS C-algebras

Given an arbitrary countably generated rigid C*-tensor category, we construct a fully faithful bi-involutive strong monoidal functor onto a subcategory of finitely generated projective bimodules over a simple, exact, separable, unital C*-algebra with a unique trace. The C*-algebras involved are built from the category using the Guionnet–Jones–Shlyakhtenko construction. Out of this category of Hilbert C*-bimodules, we construct a fully faithful bi-involutive strong monoidal functor into the category of bifinite spherical bimodules over an interpolated free group factor. The composite of these two functors recovers the functor constructed by Brothier, Hartglass, and Penneys.