Example 6.79.
For any small category \(C\), the presheaf topos \(\PSh(C)\) is essential. Indeed, the terminal morphism \(\Gamma_*\colon \PSh(C) \to \An\) is given by taking the limit \(\Gamma_*(F) = \lim_{c \in C\catop} F(c)\), and its left adjoint \(\Gamma^*\colon \An \to \PSh(C)\) sends an anima \(A\) to the constant presheaf \(\underline{A}\). The functor \(\Gamma^*\) admits a further left adjoint \(\Gamma_\sharp\colon \PSh(C) \to \An\) given by the colimit:
\[\Gamma_\sharp(F) \quad=\quad \colim_{c \in C\catop} F(c).\]