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1 results

  • 4 - Dynamical systems as dependent lenses

  • from Part I - The category of polynomial functors
  • Nelson Niu, University of Washington, David I. Spivak, Topos Institute
  • Book:
    Polynomial Functors
    Published online:
    27 September 2025
    Print publication:
    16 October 2025, pp 105-184

  • Summary

    We model discrete-time dynamical systems using a specific class of lenses between polynomials whose domains are equipped with a bijection between their positions and their directions. We introduce Moore machines and deterministic state automata as key examples, showing how these morphisms describe state transitions and interactions. We also explain how to build new dynamical systems from existing ones using operations like products, parallel composition, and compositions of these maps. This chapter demonstrates how polynomial functors can be used to represent and analyze discrete-time dynamical behavior in a clear, structured way.