Return to Question

UPDATE: I asked Victor Ostrik, and he suspects this argument is circular, in that some of the references I've cited use implicitly the commutativity of the diagram. Also, I managed to figure out a proof for the subregular case (that won't work in general).

COMMENT: My main concern with this proof attempt is that the result I'm trying to prove may actually be necessary to establish the BFO result as I stated it, i.e. maybe in the first instance $\mathrm{HC}^{ss}_{\mathbb{O}}(\mathcal{U})$ is tensor equivalent to $J^{\mathbf{c}'}$.

COMMENT: My main concern with this proof attempt is that the result I'm trying to prove may actually be necessary to establish the BFO result.

COMMENT: My main concern with this proof attempt is that the result I'm trying to prove may actually be necessary to establish the BFO result as I stated it, i.e. maybe in the first instance $\mathrm{HC}^{ss}_{\mathbb{O}}(\mathcal{U})$ is tensor equivalent to $J^{\mathbf{c}'}$.