Oberseminar (SoSe 2024/25)

This 45-minutes-talk will cover some probability monads, and generalizations. In the first section, we will encounter some classical probability monads. This will lead us to weakened products and the framework of Markov categories. As a short demonstration of this formalism, we will consider (a categorical version of) de Finetti’s theorem.
The second part then addresses generalizations: imprecise probabilities, such as Dempster-Shafer-belief functions, model situations with insufficient knowledge. Do they fit into the framework of Markov categories? Do they even have probability monads? This is still an open question. Non-commutative probability is another way of generalization; I will shortly show how this is formulated in terms of C*-algebras, and point to recent results on involutive / quantum Markov categories.