Experiments are monads (I think), but are they comonads too?

Question

I have tried to give an description of how that experiments are monads. The reason for this is that spacetimes are equivalent to interval domains, and therefore an evolutionary step in a universe is a domain map which is also a functor. The local environment (where all experiments are done) is a fixed category, and therefore the local map is an endomap and thus an endofunctor. The product $F \cdot F \rightarrow F$ handles the idea that repeated experiments go towards one monolith of data.

It seems quite natural to expect that we should also have a coproduct, $F \rightarrow F \cdot F$, implying that the endofunctor is also a comonad. The reason this seems very plausible to me is that we need copying. Experiments can be copied, so that other people can reproduce your results, and data can be copied in the normal sense. I just have not figured out what the exact mechanism should be for the copying natural transformation. What should that copying natural transformation be?

This post imported from StackExchange Physics at 2017-09-13 22:03 (UTC), posted by SE-user Ben Sprott