Owen Biesel , that doesn't seem right actually.

You seem to be taking a scheme, which is a functor \\(F: \mathcal{C} \to \mathbf{Set}\\), and then applying it *backwards* along a functor \\(G\\) mapping between the categories \\(\mathcal{D} \to \mathcal{C}\\).

If intuition serves, \\(G\\) should mapping both tables into the single table. That is to say, \\(G\\) is an inclusion of sorts.

Therefor, the instance \\((F \circ G): \mathcal{D} \to \mathbf{Set}\\) should be one big table,

\\[
\begin{array}{c|c}
\text{People} & \mathrm{FriendOf} \\\\
\hline
Alice & Bob \\\\
Bob & Alice \\\\
\vdots & \vdots \\\\
Stan & Tyler \\\\
Tyler & Stan. \\\\
\vdots & \vdots \\\\
Adele & Sara\\\\
Bertram & Antonio \\\\
\vdots & \vdots \\\\
Siegmund & Teresa \\\\
\vdots & \vdots \\\\
Antonio & Bertram \\\\
Bruno & Bertram \\\\
\vdots & \vdots \\\\
Sara & Adele \\\\
Teresa & Siegmund. \\\\
\vdots & \vdots
\end{array}
\\]

Edit: Note that \\(Tyler\\) doesn't show up twice and that his Italian friend gets mapped to someone else as a friend.