Polynomial Functors - A Mathematical Theory of Interaction

An example- and exercise-filled book for mathematical and scientific modelers with an introductory knowledge of category theory (e.g., readers of Cheng's 'Joy of Abstraction' or Fong & Spivak's 'Invitation to Applied Category Theory') interested in learning to apply the category of polynomial functors to real-world interacting dynamical systems.

List of contents

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: 6. The composition product; 7. Polynomial comonoids and retrofunctors; 8. Categorical properties of polynomial comonoids; 9. Future work in polynomial functors; References; Index.

About the author

Nelson Niu is a Ph.D. Student in the Department of Mathematics at the University of Washington. He was a keynote speaker on Polynomial Functors at the 2022 Artificial General Intelligence Conference. He conducted research in applied category theory with David I. Spivak at MIT and currently consults with NASA on category theory applied to Advanced Air Mobility Architectures.David I. Spivak is Senior Scientist and Institute Fellow at Topos Institute. He earned his Ph.D. in mathematics from UC Berkeley in 2007. He went on to demonstrate the broad applicability of category theory during his postdoctoral work and ten years at MIT. He also co-founded the Topos Institute and has authored three books on category theory applications.

Product details

• Authors: Nelson Niu, Nelson (University of Washington) Spivak Niu, Spivak David I.
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Release: 30.09.2025
• EAN: 9781009576710
• ISBN: 978-1-0-0957671-0
• No. of pages: 483
• Series: London Mathematical Society Lecture Note Series
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > Programming languages; Software Engineering, MATHEMATICS / Logic, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Maths for engineers, Mathematical logic, Set theory