Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I The category of polynomial functors
- 1 Representable functors from the category of sets
- 2 Polynomial functors
- 3 The category of polynomial functors
- 4 Dynamical systems as dependent lenses
- 5 More categorical properties of polynomials
- Part II A different category of categories
- References
- Index
4 - Dynamical systems as dependent lenses
from Part I - The category of polynomial functors
Published online by Cambridge University Press: 27 September 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I The category of polynomial functors
- 1 Representable functors from the category of sets
- 2 Polynomial functors
- 3 The category of polynomial functors
- 4 Dynamical systems as dependent lenses
- 5 More categorical properties of polynomials
- Part II A different category of categories
- References
- Index
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.
Information
- Type
- Chapter
- Information
- Polynomial FunctorsA Mathematical Theory of Interaction, pp. 105 - 184Publisher: Cambridge University PressPrint publication year: 2025
Accessibility standard: Unknown
Accessibility compliance for the PDF of this book is currently unknown
and may be updated in the future.