Alan Day and Oswald Wyler once proved that the algebras of the filter monad on the category **Top _{0}** of T

_{0}topological spaces are exactly the continuous (complete) lattices. Martín Escardó later gave a very interesting proof of this fact, using a category-theoretic construction due to Anders Kock which he calls

*KZ-monads*. My purpose is to talk about Escardó’s argument; but mostly, really, to put forward his notion of KZ-monad, which is a true categorical gem. Read the full post.