Categories and Probability Theory

[Alamino]

Does anyone know if there is any study of probability theory from the point of view of category theory? I was trying to find some references but I just found something about probabilistic automatons and precategories. I would like to see something about probability distributions and categories. Any references?

 

[matt grime]

I'm not aware of anything that might be described as a category theoretic approach to probability. I wonder what you mean by it, or, rather, what do you envisage might be the objects, morphisms and natural transformations/functors?

 

[tacman]

Yes, there is a growing area of research that combines category theory and probability theory, known as categorical probability theory. This field explores the relationship between probability and categorical structures, and has applications in various areas such as machine learning and quantum computing.

Some notable references in this field include the work of Lawvere and Schanuel on the category of distributions, and the work of Jacobs and Heunen on the categorical structure of quantum mechanics.

Additionally, there are several textbooks and lecture notes available on the topic, such as "Categorical Probability" by Fong and Spivak, and "Lectures on Categorical Probability" by Giry and Jacobs.

Overall, the study of probability theory from the perspective of category theory is a rapidly growing field with a lot of interesting research being done. I would recommend exploring some of the references mentioned above to gain a better understanding of this topic.