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arXiv · 2507.19424

Order in Partial Markov Categories

Elena Di Lavore·Mario Román·Paweł Sobociński·Márk Széles
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Abstract

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.

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Elena Di Lavore, Mario Román, Paweł Sobociński, Márk Széles. 2025-07-25. Order in Partial Markov Categories. https://doi.org/10.46298/entics.16686

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