I want to show some simple heuristic calculations which show how monad rules stem from a functor adjunction.

## Heuristic Calculations

Suppose we have some sort of duality product, and some "operators" $A$ and $A^*$.

Adjunctions means that $\langle y , A x \rangle \equiv \langle A^* y , x \rangle$

We assume …

The Reader and Writer monad are well known, but I would like to present their comonadic counterpart.