Eilenberg–Moore algebras for stochastic relations

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 identified as the positive convex structures on the base space. The forgetful functor assigning a positive convex structure the underlying Polish space has the stochastic powerdomain as its left adjoint.

Authors

• Ernst-Erich Doberkat

Keywords

• Stochastic relations
• Stochastic powerdomain
• Giry monad
• Eilenberg–Moore algebras
• Computation through monads
• Convexity
• Positive convex structures