Abstract

Markov categories are a new categorical framework for treating randomness and information flow. The basic question is: can we isolate the fundamental axioms that are sufficient to prove the theorems of probability theory? The traditional measure-theoretic approach to probability can then be seen as a semantics for this theory, possibly one out of many.

So far, several theorems of probability have been proven in this synthetic way: among them, the de Finetti theorem and the zero-one laws of Kolmogorov and Hewitt-Savage. In addition, along the way, a lot of deep concepts of probability have been given an elegant categorical description, such as the concepts of stochastic independence and of almost-sure equality.

The latest preprint on the matter is https://arxiv.org/abs/2105.02639

Joint project with Tobias Fritz, Tomas Gonda, Dario Stein, and others.