Yeah, I'm thinking that any profunctor \\(X \nrightarrow Y\\) can be flipped to give a profunctor \\(Y^\text{op} \nrightarrow X^\text{op}\\), because \\(X^\text{op} \times Y \cong (Y^\text{op})^\text{op} \times (X^\text{op})\\)... so, um, something something duality... (bit too tired to think this through right now!)