Representable Markov categories and comparison of statistical experiments in categorical probability

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this is advanced by stating proving equivalent conditions for second-order stochastic dominance, widely used way comparing distributions their spread. Furthermore, we lay foundation theory statistical experiments within classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into proof, but its abstract nature also makes result more general, automatically specializing standard Theorem in measure-theoretic as well Bayesian that involves prior-dependent garbling. Along way, define characterize representable categories, which one can talk about kernels or from spaces distributions. We do so exploring relation between Kleisli monads.