The conjecture really is compelling, however. Here's a little modification I was thinking of to get it to work.

Consider \$$\mathbf{Set}^\dagger\$$, which is the same as \$$\mathbf{Set}\$$ but without \$$\emptyset\$$.

**Puzzle MD 1.** Show that any functor \$$F: \mathbf{Set}^\dagger \to \mathbf{N}\$$ must send every morphism in \$$\textbf{Set}^\dagger \$$ to the identity morphism.