%0 Journal Article
%@ 0960-1295
%A Fritz, Tobias
%A Gonda, Tomáš
%A Houghton-Larsen, Nicholas Gauguin
%A Lorenzin, Antonio
%A Perrone, Paolo
%A Stein, Dario
%D 2023
%F discovery:10206634
%I Cambridge University Press
%J Mathematical Structures in Computer Science
%K Categorical probability; Markov category;   Semicartesian category;   Information flow;   Quasi-Borel space
%N 10
%P 913-957
%T Dilations and information flow axioms in categorical probability
%U https://discovery.ucl.ac.uk/id/eprint/10206634/
%V 33
%X 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.
%Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.