"Mild problem" - like it completely doesn't work? \\(\qquad \\)

Simon is much nicer than I am.

So is this a reasonable revised conjecture?

**Revised Conjecture.** Every functor \\(F: \mathbf{Set} \to \mathbb{N}\\) is of this form: \\(F\\) sends every object to \\(\star\\), it sends every morphism \\(f: \emptyset \to Y\\) to the same morphism \\(n : \star \to \star\\), and it sends every morphism \\(f: X \to Y\\) with \\(X \ne \emptyset\\) to the identity morphism \\(1\_\star : \star \to \star\\).

Perhaps it's better to phrase this conjecture in terms of functors from \\(\mathbf{Set}\\) to the category Simon brought in, also known as "\\(\mathbf{2}\\)": the category with two objects and one morphism from the first to the second.

Simon is much nicer than I am.

So is this a reasonable revised conjecture?

**Revised Conjecture.** Every functor \\(F: \mathbf{Set} \to \mathbb{N}\\) is of this form: \\(F\\) sends every object to \\(\star\\), it sends every morphism \\(f: \emptyset \to Y\\) to the same morphism \\(n : \star \to \star\\), and it sends every morphism \\(f: X \to Y\\) with \\(X \ne \emptyset\\) to the identity morphism \\(1\_\star : \star \to \star\\).

Perhaps it's better to phrase this conjecture in terms of functors from \\(\mathbf{Set}\\) to the category Simon brought in, also known as "\\(\mathbf{2}\\)": the category with two objects and one morphism from the first to the second.