David Spivak: Polynomial functors II: Seven wonders of the composition product

MIT Category Theory Seminar
2020/05/28

©Spifong

Speaker: David Spivak
Title: Polynomial functors II: Seven wonders of the composition product

Abstract:

On March 5 in this seminar, I discussed the category Poly of polynomial functors on Set and its applications to mode-dependent dynamical systems—machines that can change their interface and which other machines they wire to, based on their internal state.

At that time, I didn't know how to think about the composition monoidal structure on Poly in terms of dynamical systems, but it turns out that the story is quite nice. The composition product can be used to model strategies in the sense of game theory, as well as a way to "speed up" dynamical systems. But it comes with lots of other surprises too, both theoretical and applied, e.g. due to Gambino and Kock, Ahman and Uustalu, and Garner. It's a truly remarkable monoidal category.
In this talk I'll briefly review the previous one, so no special background is necessary.