Unifilarisation of stochastic Mealy machines is an instance of coalgebraic determinisation over monads with support structure, producing causal stochastic behaviours rather than Moore-style output distributions.
Ames, Sébastien Mattenet & Joe Moeller (2025):Categorical Lyapunov Theory II: Stability of Systems
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Hybrid systems expressed as coalgebras allow all standard Lyapunov stability results plus new conditions for Zeno equilibria to be instances of a single morphism theorem.
A categorical framework using lenses and tangencies provides compositional assume-guarantee reasoning for Lyapunov stability in generalized Moore machines and parameterized ODEs.
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Bayesian updates from coalgebraic determinisation
Unifilarisation of stochastic Mealy machines is an instance of coalgebraic determinisation over monads with support structure, producing causal stochastic behaviours rather than Moore-style output distributions.
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Hybrid systems expressed as coalgebras allow all standard Lyapunov stability results plus new conditions for Zeno equilibria to be instances of a single morphism theorem.
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A categorical framework using lenses and tangencies provides compositional assume-guarantee reasoning for Lyapunov stability in generalized Moore machines and parameterized ODEs.