Anindya wrote:
> could we not send one or both FriendOf in D to the identity map in C?

Anindya, I agree, one or both of FriendOf in D could be sent to the identity map in C, or FriendOf^(-1), or FriendOf composed with itself five times, etc.

Keith wrote:
> You can, but everything will get deleted unless there are Germans who are Italians (and vise versa), and they are friends with themselves (and friends' with themselves).

It sounds like you're thinking of what would happen if you took an *instance* of the D-schema and tried to interpret it as a C-schema using that functor \$$D\to C\$$. We haven't made the concept precise yet of extending a functor \$$D\to\mathbf{Set}\$$ to a functor \$$C\to\mathbf{Set}\$$ using a functor \$$D\to C\$$, so I don't know what would happen then. It sounds like you think we'd select the entries in the old database that make sense in the new database schema, and throw away the rest?