This talk will give an overview of on the one hand formalisations of basic notions from probability theory in categorical terms. The starting point here is that a conditional probability is a Kleisli map, for the discrete or continuous probability monad. This makes it possible to apply symmetric monoidal category theory and string diagrams in the area of probability theory.
On the other hand, new results will be shown that can be formulated easily in categorical terms, but that have not emerged in the traditional approach to probability theory. Further, illustrations of the use of categorical language in concrete examples will be included.
For more information there is the draft book that is close to completion: