De Finetti's Theorem in Categorical Probability

Understand

We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures.

• The proof is phrased in the language of Markov categories, which provide an abstract categorical framework for probability and information flow.
• The diagrammatic and abstract nature of the arguments makes the proof intuitive and easy to follow.
• We also show how the usual measure-theoretic version of de Finetti's Theorem for standard Borel spaces is an instance of this result.