The Universal Property of Measure-Theoretic Probability
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915683606986752 |
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| author | Rischel, Eigil Fjeldgren |
| author_facet | Rischel, Eigil Fjeldgren |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Universal Property of Measure-Theoretic Probability Rischel, Eigil Fjeldgren Category Theory Probability 60A05 (Primary) 18D10, 18B50 (Secondary) 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. |
| title | The Universal Property of Measure-Theoretic Probability |
| topic | Category Theory Probability 60A05 (Primary) 18D10, 18B50 (Secondary) |
| url | https://arxiv.org/abs/2512.15485 |