Characterizing the Eilenberg-Moore Algebras for a Monad of Stochastic Relations

Abstract

We investigate the category of Eilenberg-Moore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphisms. The algebras are characterized through convex partitions of the space of all probability measures. Examples are investigated, and it is shown that .nite spaces usually do not have algebras at all.