# De Finetti's Theorem in Categorical Probability

arXiv: https://arxiv.org/abs/2105.02639 · HTML: https://mlsanity.com/paper/2105.02639/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2021.

## Built on by (most cited first, 4 of 4)

- [A Pattern Language for Machine Learning Tasks](https://mlsanity.com/paper/2407.02424/) (2024)
- [On the Anatomy of Attention](https://mlsanity.com/paper/2407.02423/) (2024)
- [Notes on Forr'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables](https://mlsanity.com/paper/2603.24333/) (2026)
- [Topos Causal Models](https://mlsanity.com/paper/2508.08295/) (2025)

## Abstract (arXiv)

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.