Sébastien Mattenet (Université catholique de Louvain) will give a talk on
Partial enrichment as a tool for analysis in category
Abstract:
The so-called “Lyapunov’s second method” is a technique to prove the stability of dynamical systems. In it, two statements need to hold: one that a set of functions is a sound (and complete!) method for proving the stability of equilibrium points. The second that systems and Lyapunov functions can be described both in global and local terms.
This talk will start with an overview of Lyapunov’s second method and an overview of the different results from category theory on the analysis of dynamical systems. We show that Lawvere metric spaces miss most of the interesting system of Lyapunov theory and show that either more enriching or less enriching yields a satisfying analysis of stability.
We move in the setting of partial enrichment and prove the two requisite statements. Along the way, we enlarge results about comonadic categories of coalgebras.