Causal Markov Category with Kolmogorov Products
Published:Dec 30, 2025 18:58
•1 min read
•ArXiv
Analysis
This paper addresses a problem posed in a previous work (Fritz & Rischel) regarding the construction of a Markov category with specific properties: causality and the existence of Kolmogorov products. The authors provide an example where the deterministic subcategory is the category of Stone spaces, and the kernels are related to Kleisli arrows for the Radon monad. This contributes to the understanding of categorical probability and provides a concrete example satisfying the desired properties.
Key Takeaways
- •Provides a concrete example of a causal Markov category with Kolmogorov products.
- •The deterministic subcategory is the category of Stone spaces.
- •The kernels are related to Kleisli arrows for the Radon monad.
- •Explores the problem from two perspectives: pro-completions/Stone spaces and duality with Boolean algebras/effect algebras.
Reference
“The paper provides an example where the deterministic subcategory is the category of Stone spaces and the kernels correspond to a restricted class of Kleisli arrows for the Radon monad.”