Poly: An abundant categorical setting for mode-dependent dynamics

Understand

Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems.

• Previous work has shown how to allow collections of machines to reconfigure their wiring diagram dynamically, based on their collective state.
• This notion was called "mode dependence", and while the framework was compositional (forming an operad of re-wiring diagrams and algebra of mode-dependent dynamical systems on it), the formulation itself was more "creative" than it was natural.
• In this paper we show that the theory of mode-dependent dynamical systems can be more naturally recast within the category Poly of polynomial functors.