Motivated by questions in semantics of modal (propositional) logics, over the past years several duality results which extend the classical Priestley and Stone dualities were established. These results typically involve some type of Vietoris functor on topological spaces, and, by viewing spaces as (generalised) categories, in this talk we reveal the Vietories functor as part of the covariant presheaf monad. Furthermore, we show how the Kleisli construction for monads allows a common approach for this kind of duality theorems.