[Matthew](https://forum.azimuthproject.org/discussion/comment/18420/#Comment_18420), observe that \\(\mathcal{X}(\cdot, \cdot)\\) effectively gives a function \\(\mathcal{X} : \mathrm{Ob}(\mathcal{X}) \times \mathrm{Ob}(\mathcal{X}) \to \mathcal{V}\\). Therefore, the two properties on \\(\mathcal{V}\\)-enriched categories are statements about how objects in \\(\mathcal{V}\\) interact, not how objects in \\(\mathrm{Ob}(\mathcal{X})\\) interact. We do not have any obvious way of producing a monoidal structure on \\(\mathcal{X}\\).

(I would argue that, at least at this stage, a \\(\mathcal{V}\\)-enriched category is little more than a certain kind of function \\(\mathcal{X} : S \times S \to \mathcal{V}\\) from a product of sets to a monoidal preorder, since we can always recover \\(\mathrm{Ob}(\mathcal{X})\\) from the diagonal elements \\((x, x) \in \mathrm{Dom}(\mathcal{X})\\).)