Algebras of filter-related monads: II. KZ-monads

Alan Day and Oswald Wyler once proved that the algebras of the filter monad on the category Top₀ of T₀ 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.