>**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}\\).

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}\\).