> **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}} \$$.