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.