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. This abstraction allows for multiple versions of the original theorem to arise as consequences merely by interpreting the categorical result in different Markov categories. Moreover, the diagrammatic and abstract nature of the arguments makes the proof intuitive and easy to follow.

中文翻译：

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De Finetti分类概率定理

我们提出了de Finetti定理的新颖证明，它描述了变量无穷序列的置换不变概率测度，即所谓的可交换测度。该证明用马尔可夫类别的语言表述，该类别为概率和信息流提供了一个抽象的分类框架。这种抽象仅通过解释不同马尔可夫类别中的分类结果就可以将原始定理的多个版本作为结果出现。此外，论证的图示性和抽象性使证明直观且易于遵循。