Rigid C*-tensor categories of bimodules over interpolated free group factors

Given a countably generated rigid C*-tensor category ${\sf C}$C, we construct a planar algebra P• whose category of projections ${\sf Pro}$Pro is equivalent to ${\sf C}$C. From P•, we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid C*-tensor category ${\sf Bim}$Bim whose objects are bifinite bimodules over an interpolated free group factor, and we show ${\sf Bim}$Bim is equivalent to ${\sf Pro}$Pro. We use these constructions to show ${\sf C}$C is equivalent to a category of bifinite bimodules over $L(\mathbb {F}_\infty )$L(F∞).