We eventually sorted this out, and it appears as (one direction of) Theorem 3.6.7. in Dualizable Tensor Categories (joint with Christopher Douglas and Chris Schommer-Pries). Note that separability equivalent to semisimplicity of C and Z(C) (see Corollary 3.5.9.).
Noah Snyder
- 28.1k
- 4
- 94
- 170