Ahman et al. wrote about when a container is a comonad. Containers are also monads, such as List. This means that we can take all containers that are endofunctors on Set and they live in the endofunctor category on set. This category has a monoidal product, which is functor composition. Thus we can have a monoidal category for containers that are either monads or comonads. This must have a diagrammatic calculus. What are the axioms of this diagrammatic calculus?

I thought for a second this doesn't work because you can't compose all the functors for all containers....though they are all endofunctors so they should compose. I was just thinking of composing Tree with List, but That should work you just get a tree of lists.