>**Puzzle 101.** There are certain sets \$$S\$$ such that there's at most one function from any set to \$$S\$$ and also at most one function from \$$S\$$ to any set. If we take sets of this sort and functions between them, we get a "subcategory" of \$$\mathbf{Set}\$$ that's actually a preorder. What is this preorder like?

The set with at most one function out of it is the *empty set*, \$$\varnothing\$$, and the set with at most one function into it is any one element set, \$$\mathbb{1}\$$.

A preorder, with \$$\varnothing\$$ as the bottom element and any \$$\mathbb{1}\$$ as the top element is equivalent to preorder \$$\mathbf{Bool}\$$.