  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.
