eprintid: 10206634
rev_number: 7
eprint_status: archive
userid: 699
dir: disk0/10/20/66/34
datestamp: 2025-03-28 09:22:15
lastmod: 2025-03-28 09:22:15
status_changed: 2025-03-28 09:22:15
type: article
metadata_visibility: show
sword_depositor: 699
creators_name: Fritz, Tobias
creators_name: Gonda, Tomáš
creators_name: Houghton-Larsen, Nicholas Gauguin
creators_name: Lorenzin, Antonio
creators_name: Perrone, Paolo
creators_name: Stein, Dario
title: Dilations and information flow axioms in categorical probability
ispublished: pub
divisions: UCL
divisions: B04
divisions: F48
keywords: Categorical probability; Markov category; 
Semicartesian category; 
Information flow; 
Quasi-Borel space
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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.
date: 2023-11
date_type: published
publisher: Cambridge University Press
official_url: https://doi.org/10.1017/s0960129523000324
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 2357363
doi: 10.1017/S0960129523000324
lyricists_name: Lorenzin, Antonio
lyricists_id: ALORE86
actors_name: Lorenzin, Antonio
actors_id: ALORE86
actors_role: owner
funding_acknowledgements: P 35992-N [Austrian Science Fund (FWF)]; Y 1261-N [START Prize of the Austrian Science Fund (FWF)]; [Sam Staton's grant BLaSt - a Better Language for Statistics of the European Research Council (ERC)]
full_text_status: public
publication: Mathematical Structures in Computer Science
volume: 33
number: 10
pagerange: 913-957
pages: 45
issn: 0960-1295
citation:        Fritz, Tobias;    Gonda, Tomáš;    Houghton-Larsen, Nicholas Gauguin;    Lorenzin, Antonio;    Perrone, Paolo;    Stein, Dario;      (2023)    Dilations and information flow axioms in categorical probability.                   Mathematical Structures in Computer Science , 33  (10)   pp. 913-957.    10.1017/S0960129523000324 <https://doi.org/10.1017/S0960129523000324>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10206634/1/Fritz%20Gonda%20Houghton-Larsen%20Lorenzin%20Perrone%20Stein%20-%20Dilations%20and%20information%20flow%20axioms%20in%20categorical%20probability.pdf