Example 6.71.
If \(C\) admits a terminal object \(1\), then \(\PSh(C)\) has dimension \(\leq 0\). Indeed, global sections are given by evaluation at \(1\), and evaluation preserves effective epimorphisms. Equivalently, if \(\Ff\) is \((-1)\)-connected, then \(\Gamma_*(\Ff) \iso \Ff(1)\) is nonempty. See [Lurie 2009, Example 7.2.1.3].
References
- Jacob Lurie. Higher topos theory. Ann. Math. Stud. 170, Princeton, NJ: Princeton University Press. 2009.