> **Puzzle 103.** Figure out the best way to take any category \$$\mathcal{C}\$$ and "squash it down", getting a preorder whose elements are the objects of \$$\mathcal{C}\$$.

I would define \$$\leq_{\mathcal{C}}\$$ with:

\$X \leq_{\mathcal{C}} Y \equiv \mathrm{Hom}(X,Y) \neq \varnothing \$

Where \$$\mathrm{Hom}(X,Y)\$$ is the [set of morphisms](https://en.wikipedia.org/wiki/Morphism#Hom-set) between \$$X\$$ and \$$Y\$$.

If \$$\mathcal{C}\$$ is already a preorder, this doesn't do anything to it.