With respect to Proposition 3.95, if \(\mathcal{J}=0\), then \(n=0\); there are no vertices.
There is exactly one empty tuple which vacuously satisfies the properties, so we’ve constructed the limit as the singleton set \(\{()\}\) consisting of just the empty tuple.
Thus the limit of the empty diagram, i.e. the terminal object in Set, is the singleton set.