F. Marmolejo

A basic distributive law

Abstract We pursue distributive laws between monads, particularly in the context of KZ-doctrines, and show that a very basic distributive law has (constructively) completely distributive lattices for its algebras. Moreover, the resulting monad is shown to be also the double dualization monad (with respect to the subobject classifier) on ordered sets.

Beck's theorem for pseudo-monads

In this work we establish a 2-categorical analogue of Becks theorem characterizing monadic functors. We show that a 2-functor (a pseudo-functor) U is monadic iff it is a right pseudo-adjoint, it reflects adjoint equivalences and it creates U-absolute pseudo-coequalizers of codescent objects