Categorical characterization of probability product measure Product probability measure as invariant morphism (Japanese)

regular conditional probability measure, transition probability.

https://m-hiyama.hatenablog.com/entry/20170329/1490772264

If we restrict morphism to product measure, it becomes directed graph.
(p x r) (r x q) = p x q.
In particular, (p x 1) (1 x q) = p x q.
Embedding is right inverse mapping of forgetful functor, but it is not functor.