Abstract: Markov categories are a new mathematical framework designed to deal with problems in probability and statistics, using a higher abstraction layer. For an analogy, high-level programming languages (such as Python) allow the user to write code without worrying about lower-level issues such as memory allocation. Similarly, Markov categories allow the user to write rigorous mathematics, possibly involving continuous sample spaces and singularities, without having to know any measure theory. Moreover, they come equipped with a graphical formalism which faithfully reflects the information flow and the stochastic dependencies, and so they give a very general theory of graphical models.

Several concepts of probability and statistics have already been incorporated into the formalism, and sometimes restated and reproven in
a more general way. Among these we have conditioning, filtering, de Finetti’s theorem, Blackwell’s theorem on statistical experiments, Shannon’s entropy and information inequalities, and d-separation theorems. This is an active field of research, and more and more results are added by the day.

In this talk I will give an introduction to the part of this formalism which is already developed and ready to be used. I will assume no prerequisite knowledge of category theory.