Joint stalk functor on sheaves of sets ($F\mapsto (F_x{)}_{x\in X}$)

The joint stalk functor $\mathbf{Sh}(X)\to {\mathbf{Set}}^X$ is faithful: equality of germs makes two images of a section locally equal, and the sheaf uniqueness axiom makes them globally equal. Its right adjoint is the product of the set-valued skyscraper sheaves at all points. The Beck comonadicity theorem then makes the joint stalk functor comonadic.