I meant to write \$$\Psi\Phi \colon \mathcal{X}^{\text{op}} \times \mathcal{Z} \to \mathcal{V} \$$ rather than \$$\Psi\Phi \colon \mathcal{X}^{\text{op}} \times \mathcal{Y} \to \mathcal{V} \$$. My mistake!