Webpage of the Compositional Systems and Methods group at TalTech.

**Eigil Rischel**, University of Copenhagen

0-1 Laws and category theory

I will present some recent work in the application of category theory to probability. Kolmogorov’s zero to one law is a classical result in probability theory, stating that, given an infinite family of independent random variables, and a statement about them which is independent of any finite subset of them, the probability that this statement holds is either zero or one. I will give a brief overview of the measure theory that goes into the classical version of this theorem. Then I will discuss how to state and prove an abstract version of this theorem, in the context of “synthetic” probability theory. If time permits, I will survey some work in process which continues this line of research.