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- W4308505242 abstract "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." @default.
- W4308505242 created "2022-11-12" @default.
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- W4308505242 date "2022-11-04" @default.
- W4308505242 modified "2023-10-14" @default.
- W4308505242 title "Dilations and information flow axioms in categorical probability" @default.
- W4308505242 doi "https://doi.org/10.48550/arxiv.2211.02507" @default.
- W4308505242 hasPublicationYear "2022" @default.
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