2502.15276
Categorical Lyapunov Theory I: Stability of Flows
Aaron D. Ames, Joe Moeller, Paulo Tabuada
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate reproduces the paper’s Categorical Lyapunov theorem and its converse with the same hypotheses and constructions (class-K bounds with invertible α, decrescence; V := sup_T ||ϕ|| with local suprema commuting with whiskering). The logical steps and needed assumptions align with the paper’s proofs.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper provides a rigorous categorical framework for Lyapunov stability of flows and proves necessity and sufficiency of Lyapunov morphisms under clear axioms. The arguments are sound, well-scaffolded by diagrams, and illustrated with classical and enriched examples. Minor clarifications (class-K invertibility and whiskering of suprema) would improve accessibility for readers transitioning from classical control to categorical language.