A mathematical framework for causality

This thesis studies a categorical approach to probabilistic and causal models, by building on established frameworks. It first introduces the necessary groundwork in category theory, defining monoidal and symmetric monoidal categories and stating coherence results that ensure precise correspondences between algebraic identities and string diagrammatic representations. It then views probability theory under categorical lens, setting the stage for a categorical definition of Bayesian networks. It also introduces causal theories as suitable categories, and defines causal models characterizing their structure. Finally, it formalizes interventional distributions as certain functors, and gives a procedure to recover such distributions from observational data.