Mikhael Gromov - 5/6 Probability, symmetry, linearity

I plan six lectures on possible directions of modification/generalization of the probability theory, both concerning mathematical foundations and applications within and without pure mathematics. Specifically, I will address two issues. 1. Enhancement of stochastic symmetry by linearization and Hilbertization of set-theoretic categories. 2. Non-symmetric probability theory in heterogeneous environments of molecular biology and of linguistics. I will start with a category theoretic view on probability