[Keith wrote:](https://forum.azimuthproject.org/discussion/comment/19054/#Comment_19054)
> For one thing, we never explicitly gave a functor from \$$\mathbf{Set}\$$ to \$$\mathbb{N}\$$, even though \$$\mathbb{N}\$$ is certainly a category.

Can you elaborate on why we ought to consider \$$\mathbb{N}\$$ as a category in this context? It seems we're only counting things, so a mere function \$$\mathrm{Ob}(C) \to \mathbb{N}\$$ seems appropriate.