[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.

> 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.