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Polynomial Functors: A General Theory of Interaction

This webpage is for a course that was run in 2021. Although the course is now finished, recordings of the lectures can be found below, along with a link to the book.


The category of polynomial functors is a fascinating setting, brimming with rich mathematics and tantalizing applications. In this course, we will investigate these polynomials, with emphasis on their applications to dynamical systems, decisions, and data. We aim to strike a balance between a solid theoretical foundation and a breadth of examples.

Instructors: Nelson Niu & David Spivak


Polynomial Functors: A General Theory of Interaction

A work-in-progress! Feedback is welcome and may be shared here. Class discussions will likely inform how we present this content within the book and in future work.


The YouTube playlist of all recorded lectures and future livestreams can be found here.


You should be able to define the following fundamental concepts from category theory:

We'll discuss the following as if you've seen them before but may need a quick refresher: