The composite \(\mathcal{X}\overset{\phi;\psi}\nrightarrow \mathcal{Z}\) of two \(\mathcal{V}\) profunctors, \(\mathcal{X}\overset{\phi}\nrightarrow\mathcal{Y}\) and \(\mathcal{Y}\overset{\psi}\nrightarrow\mathcal{Z}\)
\((\phi;\psi)(x,z) = \bigvee_Y(\phi(x,y)\otimes\psi(y,z))\)