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This colloquium talk from the Topos Institute explores a categorical framework for generalizing Lyapunov stability theory in dynamical systems. Discover how Joe Moeller extends Lyapunov's 1892 methodology, which allows for certifying the stability of equilibrium points without solving differential equations directly. Learn about the innovative approach that uses coalgebras of endofunctors to represent dynamical systems and internal monoid actions to represent their solutions. The presentation introduces the concept of "Lyapunov morphisms" and demonstrates how this generalization recovers both classical continuous and discrete time versions of Lyapunov's theorem, while extending to dynamics in Lawvere metric spaces and quantale-enriched categories. Gain insights into this mathematical framework that forms the foundation of modern nonlinear control theory.
