Order in Partial Markov Categories
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917300146274304 |
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| author | Di Lavore, Elena Román, Mario Sobociński, Paweł Széles, Márk |
| author_facet | Di Lavore, Elena Román, Mario Sobociński, Paweł Széles, Márk |
| contents | Partial Markov categories are a recent framework for categorical probability theory that provide an abstract account of partial probabilistic computation with updating semantics. In this article, we discuss two order relations on the morphisms of a partial Markov category. In particular, we prove that every partial Markov category is canonically preorder-enriched, recovering several well-known order enrichments. We also demonstrate that the existence of codiagonal maps (comparators) is closely related to order properties of partial Markov categories. Finally, we introduce a synthetic version of the Cauchy--Schwarz inequality and, from it, we prove that updating increases validity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Order in Partial Markov Categories Di Lavore, Elena Román, Mario Sobociński, Paweł Széles, Márk Logic in Computer Science 18M05 Partial Markov categories are a recent framework for categorical probability theory that provide an abstract account of partial probabilistic computation with updating semantics. In this article, we discuss two order relations on the morphisms of a partial Markov category. In particular, we prove that every partial Markov category is canonically preorder-enriched, recovering several well-known order enrichments. We also demonstrate that the existence of codiagonal maps (comparators) is closely related to order properties of partial Markov categories. Finally, we introduce a synthetic version of the Cauchy--Schwarz inequality and, from it, we prove that updating increases validity. |
| title | Order in Partial Markov Categories |
| topic | Logic in Computer Science 18M05 |
| url | https://arxiv.org/abs/2507.19424 |