Exactly.

To generalize beyond monoidal preorders, we can write \\(\mathbb{ECP}\\) in terms of 'change of base' that John talked about around Puzzle 94 in [Lecture 33](https://forum.azimuthproject.org/discussion/2192/lecture-33-chapter-2-tying-up-loose-ends).

> - An object is a pair \\((\mathcal{V}, \mathcal{X})\\) where \\(\mathcal{V}\\) is a monoidal preorder and \\(\mathcal{X}\\) is an enriched category over \\(\mathcal{V}\\).
>
> - A morphism \\((\mathcal{V}, \mathcal{X}) \to (\mathcal{U}, \mathcal{Y})\\) consists of a pair \\(\left( f\colon \mathcal{V}\to \mathcal{U}, \,\, F\colon \mathcal{X}_f \to \mathcal{Y}\right)\\) where \\(f\\) is a monoidal preorder map and \\(F\\) is a \\(\mathcal{U}\\)-functor.