@Matthew – I don't understand this line:

> Based on [Lecture 60](https://forum.azimuthproject.org/discussion/2287/lecture-60-chapter-4-closed-monoidal-posets), to make \$$\mathrm{hom}\$$ a \$$\mathcal{V}\$$-enriched functor we want \$$\mathcal{Y} = - \multimap - \$$.

Surely we just set \$$\mathcal{Y}\$$ to be \$$\mathcal{V}\$$ (considered as a \$$\mathcal{V}\$$-enriched category)?

EDIT to add: oh wait, I see, you mean the function \$$(y, y') \mapsto \mathcal{Y}(y, y')\$$ should be \$$(- \multimap -)\$$

EDIT to add: in which case I think this line is wrong:

> $(\mathcal{X}^{\text{op}} \times \mathcal{X})((a,b),(c,d)) = \mathcal{X}(b,a) \otimes \mathcal{X}(c,d)$

$(\mathcal{X}^{\text{op}} \times \mathcal{X})((a,b),(c,d)) = \mathcal{X}^\text{op}(a, c) \otimes \mathcal{X}(b, d) = \mathcal{X}(c, a) \otimes \mathcal{X}(b, d)$