The last post was late. Let me compensate by being early this time.
I had promised you that we would see why the theory of the Hoare powerspace monad was given by a small family of axioms, those of unital inflationary semilattices. I will substantiate this claim in two ways. Following Andrea Schalk, we shall see that H(X) is the free such (sober) thing over X, and we shall see that those (sober) things are exactly the algebras of the H monad—a nice way to introduce the notion of algebra of a monad. Read the full post.