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arXiv · 2512.15485

The Universal Property of Measure-Theoretic Probability

Eigil Fjeldgren Rischel
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Abstract

Building on work of Chen, we give a universal property of the Markov category BorelStoch of standard Borel spaces and Markov kernels between them. To do this, we introduce a new notion of *coinflip*, or unbiased binary choice, in a Markov category. These are unique if they exist, and automatically preserved by all Markov functors which preserve coproducts. We also provide universal characterizations of various Markov categories of discrete kernels.

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Eigil Fjeldgren Rischel. 2025-12-17. The Universal Property of Measure-Theoretic Probability. https://arxiv.org/abs/2512.15485

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