Pattern runs on matter

Abstract

Interviews run on people, programs run on computers, voting schemes run on voters, games run on players. Each of these is an example of the abstraction “pattern runs on matter”. In these cases, pattern determines the flow of how a situation might unfold, while matter responds with decisions at each juncture. In this talk, we will show how the free monad monad in the category of polynomial functors with the substitution monoidal product represents “pattern” while the cofree comonad represents “matter”. Lastly, “runs on” is represented by a naturally arising interaction law between a free monad and a cofree comonad.