re **Puzzle 87**, @John mentioned that the "process of deducing" the answer is important... so I thought it might be instructive to simply replace \$$\mathcal{V}\$$ with \$$\mathbf{Bool}\$$ in his definition to see where it gets us:

> A **\$$\mathbf{Bool}\$$-enriched category** \$$\mathcal{X}\$$ consists of two parts, satisfying two properties. First:
>
> 1. one specifies a set \$$\mathrm{Ob}(\mathcal{X})\$$, elements of which are called **objects**;
>
> 2. for every two objects \$$x,y\$$, one specifies an element \$$\mathcal{X}(x,y)\$$ of \$$\mathbf{Bool}\$$.
>
> Then:
>
> a) for every object \$$x\in\text{Ob}(\mathcal{X})\$$ we require that
>
> ${\tt{true}} \leq \mathcal{X}(x, x)$
>
> b) for every three objects \$$x,y,z\in\mathrm{Ob}(\mathcal{X})\$$, we require that
>
> $\mathcal{X}(x,y)\wedge \mathcal{X}(y,z)\leq\mathcal{X}(x,z)$

It's pretty clear that (a) is equivalent to \$\mathcal{X}(x, x) = \tt{true}\$ and (b) is equivalent to \$\mathcal{X}(x,y) = {\\tt{true}} {\textrm{ and }} \mathcal{X}(y,z) = {\\tt{true}} {\textrm{ implies }} \mathcal{X}(x,z) = {\\tt{true}}\$ ie, the reflexive and transitive laws.