Cartesian monads on toposes
A geometric morphism between toposes, being an adjoint pair of left exact functors, induces a left exact monad on the codomain. The author addresses the question whether any left exact monad on a topos arises this way. The answer is positive provided the topos is Boolean. The proof technique is: use the existing theory of strong and indexed monads to reduce the question to the case where the topos is the category of \({\mathcal S}ets\). Here, left exact monads are shown to correspond bijectively to strongly zero dimensional locales, and these give rise to the desired geometric morphisms.
scientific article; zbMATH DE number 1004400