You may have a point.

So then \\(G\\) is more like a mapping between the underlying graphs of the categories than a mapping between databases themselves.

Though, \\(G\\) can be used to *make* a database, but only after we compose it with some \\(F: \mathcal{C} \to \mathbf{Set}\\) to get the database instance, \\((F \circ G): \mathcal{D} \to \mathbf{Set}\\).

So then \\(G\\) is more like a mapping between the underlying graphs of the categories than a mapping between databases themselves.

Though, \\(G\\) can be used to *make* a database, but only after we compose it with some \\(F: \mathcal{C} \to \mathbf{Set}\\) to get the database instance, \\((F \circ G): \mathcal{D} \to \mathbf{Set}\\).