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.