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