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Explore the mathematical foundations of information cohomology in this Topos Institute Colloquium talk that delves into how various information functions can be understood through cohomological structures. Learn about Shannon entropy of discrete probability measures, differential entropy, and the dimension of continuous measures within this theoretical framework. Gain insights into the fundamental concepts requiring only basic knowledge of category theory and homological algebra. Discover the connections between Renyi's information dimension, geometric invariants of manifold-valued laws, and entropy concepts for categories, including Leinster's diversity of metric spaces. The presentation covers both established results in information cohomology since its 2015 introduction by Baudot and Bennequin, as well as current open problems and future research directions in this fascinating intersection of mathematics and information theory.
