Stochastic function

The category of stochastic functions is the Kleisli category of the distribution monad.

• Cartesian, partial and stochastic
• Independent marginalization for a strong monad
• distribution monad

References

• A Synthetic Approach to Markov Kernels (Fritz, 2020), uses the finitary version.
• A Presentation of the Category of Stochastic Matrices (Fritz), presents the finite version.
• Evidential Decision Theory via Partial Markov Categories (Di Lavore, Roman, 2023)
• Partial Markov Categories (Di Lavore, Roman, Sobocinski, 2025)