TY  - JOUR
Y1  - 2023/11//
AV  - public
EP  - 957
TI  - Dilations and information flow axioms in categorical probability
PB  - Cambridge University Press
N2  - 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.
ID  - discovery10206634
KW  - Categorical probability; Markov category; 
Semicartesian category; 
Information flow; 
Quasi-Borel space
VL  - 33
SP  - 913
IS  - 10
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
UR  - https://doi.org/10.1017/s0960129523000324
SN  - 0960-1295
A1  - Fritz, Tobias
A1  - Gonda, Tomá?
A1  - Houghton-Larsen, Nicholas Gauguin
A1  - Lorenzin, Antonio
A1  - Perrone, Paolo
A1  - Stein, Dario
JF  - Mathematical Structures in Computer Science
ER  -