As an exceptionally silly case, what does a **Unit**-enriched category look like? **Unit** is the single-element set \\(\\{\cdot\\}\\) with the trivial preorder -- the only one it could have, after all -- and the natural monoidal structure -- again, the only one it could possibly have.

For a given set \\(S\\), we can define the **Unit**-enriched category \\(\mathcal{X}\\) by \\(\mathrm{Ob}(\mathcal{X}) = S\\) and \\(\mathcal{X}(x, y) = \cdot\\) for all \\(x, y \in S\\). This satisfies both conditions trivially.

I'm tempted to identify this construction with the codiscrete preorder on \\(S\\).