Teoria categorial das probabilidades

This work aims to present some of the main concepts of the categorical approach to probability theory. We first lay down some prerequisites definitions and results from classical probability theory (measure theoretic) and category theory, then we define two main approaches to the subject: One, the first one historically and most classic, via Giry monads and then moves to the more recent concept of a Markov category. At the end, we show a recent result that is an analogue to classical decomposition theorems in ergodic theory.