Powers of polynomial monads

I never much cared for exponentiation in . The category of polynomial functors has tons of different operations, and I had my favorites. When it comes to database migration, wiring diagrams, discrete dynamical systems, etc., the most important operations seemed to be and . Sure, we build polynomials out of and , but about I’d ask: “what have you done for me lately?"

This is a companion discussion topic for the original entry at https://topos.site/blog/2023-09-21-powers-of-polynomial-monads/