| Markov category | Probability monad | Conditionals | Positivity | Kolmogorov products | Further references |
|---|---|---|---|---|---|
| Stoch | Giry monad on SoberMeas | No (Fritz'20, Example 11.3) | Yes (Fritz'20, Example 11.25) | Not in general | Fritz'20 |
| BorelStoch | Giry monad on BorelMeas | Yes (Kallenberg '17, B-M'19) | Yes (Fritz'20, Section 11) | Countable (Fritz-Rischel'19) | Fritz'20 |
| FinStoch | Not representable (closely related to the distribution monad) | Yes (Fritz'20, Example 11.6) | Yes (Fritz'20, Section 11) | No | Fritz'20 |
| TychStoch | probability monad on topological spaces (here, Tychonoff) | No | Yes (Fritz et al'23) | ? | Fritz et al'23 |
| QBStoch | probability monad on quasi-Borel spaces | No (Sabok et al'20) | No (Sabok et al'20) | ? | Fritz et al'23 |
| Gauss | ? | Yes (Fritz'20) | Yes (Fritz'20) | No | Stein et al.'23 |
| FinSetMulti | Finite nonempty power set monad | Yes (Fritz'20) | Yes (Fritz'20) | No (Fritz-Rischel'19) | Stein et al.'23 |
(…to be expanded…)
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