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Explore the categorical foundations of probability theory through a mathematical seminar that develops a systematic descent theory for probabilistic structures. Delve into how coarse-graining and quotient formation—fundamental concepts across mathematics from topology to algebra—can be rigorously applied to probability theory where "observing" random variables creates quotients of sample spaces. Examine how this new theoretical framework unifies three core probabilistic concepts: measurability, disintegration, and stochastic dominance within a single coherent structure. Learn how this approach parallels classical categorical descent theory while accounting for the unique challenges posed by stochastic dependence and correlations in probabilistic settings. Gain conceptual understanding of the deep relationships between random variables, statistical experiments, and inference procedures through this categorical lens. Discover how this systematic treatment respects established probabilistic practice while providing new theoretical insights into the nature of randomness as "ignorance" and the role of sigma-algebras in modeling probabilistic observations.
