Polynomial Functors - Theory and Applications to Dynamical Systems and Data

Explore the mathematical theory and applications of polynomial functors through this comprehensive 15-hour 46-minute course from the Topos Institute, taught by David Spivak and Nelson Niu. Delve into the category of polynomial functors, examining their rich mathematical properties and practical applications to dynamical systems and data analysis. Master fundamental concepts including polynomial morphisms, dynamics of polynomials, and the double category of arenas while building a solid theoretical foundation. Investigate advanced topics such as categorical properties of polynomials, composition products, polynomial comonoids as categories, and cofunctors. Learn about cofree polynomial comonoids, products of polynomial comonoids, and bimodules over polynomial comonoids as parametric right adjoints. Study how behaviors compose through matrix arithmetic and explore the connections between polynomial functors and category theory. Benefit from live-streamed lectures with automatic recordings available afterward, balancing rigorous mathematical theory with a breadth of practical examples throughout the curriculum.