Categorical probability explained

In mathematics, categorical probability is a category-theoretic approach to probability theory. The idea goes back to at least Lawvere's 1962 paper.^[1]

Some constructs in the theory are

• The category of measurable spaces
• Markov category

a motivating example is the category of Markov kernels.

• Probability monad such as Giry monad.

References

• https://ncatlab.org/nlab/show/category-theoretic+approaches+to+probability+theory
• https://golem.ph.utexas.edu/category/2024/07/imprecise_probabilities_toward.html#more

Further reading

• https://ncatlab.org/nlab/show/Giry+monad#related_constructions
• Voevodsky's unfinished manuscript: Notes on categorical probability, July 13, 2009.

External links

• https://golem.ph.utexas.edu/category/2020/06/categorical_probability_and_st.html
• https://golem.ph.utexas.edu/category/2020/06/statistics_for_category_theori.html

Notes and References

1. W. Lawvere, The category of probabilistic mappings, 1962.