Example 4.12.
For \(C = \emptyset\), we get \(\emptyset^{\lex} = *\) and so \(\An[\emptyset] = \PSh(*) = \An\). In particular, \(\An\) is the initial logos:
\[\Fun_{\bbLog}(\An,T) \quad \simeq \quad \Fun(\emptyset,T) \quad \simeq \quad *.\]
By dualizing, it follows that \(\An \in \Topos\) is the terminal topos.