Consider the schema \(\mathfrak{g} := \boxed{\overset{Email}\bullet \overset{sentBy}{\underset{receivedBy}{\rightrightarrows}} \overset{Address}\bullet}\)
And an example instance: \(\mathfrak{g}\xrightarrow{I}\mathbf{Set}\)
| SentBy | ReceivedBy | |
|---|---|---|
| 1 | Bob | Grace |
| 2 | Grace | Pat |
| 3 | Bob | Emmy |
| 4 | Sue | Doug |
| 5 | Doug | Sue |
| 6 | Bob | Bob |
Data migration functors \(\Sigma_!,\Pi_!\) go from \(\mathcal{C}\) Inst to 1-Inst, but we showed that 1-Inst is equivalent to Set in Example 3.53.
\(\Sigma_!\) tells us the mailing groups, the "connected components" in \(I\):
| 1 |
|---|
| Bob-Grace-Pat-Emmy |
| Sue-Doug |
\(\Pi_!\) tells us the emails that were sent from a person to themselves
| 1 |
|---|
| \(Em_6\) (Bob) |