# Categorical Lyapunov Theory II: Stability of Systems

arXiv: https://arxiv.org/abs/2505.22968 · HTML: https://mlsanity.com/paper/2505.22968/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2025.

## Built on by (most cited first, 1 of 1)

- [LC-SAC: Lyapunov-Constrained Soft Actor-Critic via Koopman Operator Theory for Trajectory Tracking and Stabilization](https://mlsanity.com/paper/2602.04132/) (2026)

## Abstract (arXiv)

Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which we can study the stability of a coalgebra for an endofunctor F. One is minimal and better suited for concrete settings, while the other is more intricate and provides a richer theory. We prove a Lyapunov theorem for both notions of setting for stability, and a converse Lyapunov theorem for the second.