John asked in [comment 26](https://forum.azimuthproject.org/discussion/comment/19268/#Comment_19268):

> **Puzzle.** Can we change the category \\(\mathcal{C}\\) to a category \\(\mathcal{C}^\prime\\) so that functors \\(F : \mathcal{C}^\prime \to \mathbf{Set}\\) are just databases of the sort Keith drew, with the kind of symmetry that his table has?

I think we need to add the further constraint that \\( \textrm{FriendOf} \circ \textrm{FriendOf} = 1_{\textrm{People}} \\).

> **Puzzle.** Can we change the category \\(\mathcal{C}\\) to a category \\(\mathcal{C}^\prime\\) so that functors \\(F : \mathcal{C}^\prime \to \mathbf{Set}\\) are just databases of the sort Keith drew, with the kind of symmetry that his table has?

I think we need to add the further constraint that \\( \textrm{FriendOf} \circ \textrm{FriendOf} = 1_{\textrm{People}} \\).