Dilations and information flow axioms in categorical probability

Autor:	Fritz, Tobias, Gonda, Tomáš, Houghton-Larsen, Nicholas Gauguin, Lorenzin, Antonio, Perrone, Paolo, Stein, Dario
Rok vydání:	2022
Předmět:	Mathematics - Category Theory Computer Science - Information Theory Computer Science - Logic in Computer Science Mathematics - Probability 18M05 18D10 60A05 68Q55 03B70
Zdroj:	Mathematical Structures in Computer Science 33(10), 913-957 (2023)
Druh dokumentu:	Working Paper
DOI:	10.1017/S0960129523000324
Popis:	We study the positivity and causality axioms for Markov categories as properties of dilations and information flow in Markov categories, and in variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity, but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation. Comment: 42 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.02507 Zobrazit plný text záznamu View this record from Arxiv