Codensity and stone spaces

Abstract

Abstract We present a detailed computation of two codensity monads associated to two canonical functors – the inclusion functor of FinSet into Top and the inclusion functor of the category of the powers of the Sierpiński space into Top. We show that the categories of algebras of the two monads are the categories of Stone spaces and of sober spaces, respectively. A new motivation for defining these classes of spaces is therefore obtained.