Journal article
Dilations and information flow axioms in categorical probability
- Abstract:
- We study the positivity and causality axioms for Markov categories as properties of dilations and information flow and also develop 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 602.9KB, Terms of use)
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- Publisher copy:
- 10.1017/s0960129523000324
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Mathematical Structures in Computer Science More from this journal
- Volume:
- 33
- Issue:
- 10
- Pages:
- 913-957
- Publication date:
- 2023-10-25
- Acceptance date:
- 2023-09-11
- DOI:
- EISSN:
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1469-8072
- ISSN:
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0960-1295
- Language:
-
English
- Keywords:
- Pubs id:
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1561173
- Local pid:
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pubs:1561173
- Deposit date:
-
2024-05-09
Terms of use
- Copyright holder:
- Fritz et al.
- Copyright date:
- 2023
- Rights statement:
- © The Author(s), 2023. Published by Cambridge University Press.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Cambridge University Press at https://dx.doi.org/10.1017/s0960129523000324
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