Matthew

Yeah I knew the first part of the proof was dubious at best when I was writing it out. Like you said it's pretty obvious what's going on with the objects but I just didn't know how to prove it and the above result was the best I could do.

Wait, the problem asks to show \$$\Psi\Phi \colon \mathcal{X}^{\text{op}} \times \mathcal{Y} \to \mathcal{V} \$$ is a \$$\mathcal{V}\$$-enriched category? Why isn't it \$$\Psi\Phi \colon \mathcal{X}^{\text{op}} \times \mathcal{Z} \to \mathcal{V} \$$? Maybe I don't get what's going on with the objects...