Compact-closedness conjecture for pointed bimodular profunctors

Let $𝕄$ be a monoidal category, and let $𝕄^{\mathrm{Rev}}$ denote its reverse monoidal category, with tensor product

$$A \otimes_{Rev} B = B \otimes A.$$

The objects, 1-cells, 2-cells and 3-cells of the tricategory of pointed bimodular profunctors are as defined in the paper. Compact-closedness conjecture. Pointed bimodular profunctors form a compact closed tricategory, with the dual of each monoidal category given by its reverse monoidal category $𝕄^{\mathrm{Rev}}$. This would extend the string-diagrammatic framework developed in the paper and provide duality data for the tricategory; establishing the required compact-closed coherence remains further work.