Hi, I have a question regarding the connection between monads and comonads. I always thought of the comonad operations as being the inverse operations of the corresponding monad functions. As I do not know the underlying theory I thought I simply ask the masters. Is there a formal verification for this intuition? That is, are there always corresponding instances for monad and comonad such that the following laws are satisfied? extract . return == id join . duplicate == id If this is the case I would like to know what the corresponding monad for the following comond could be. This comonad treats lists as pointed sets where the first element is focused. instance Comonad [] where extract = head duplicate xs = init (zipWith (++) (tails xs) (inits xs)) Obviously we can define return x = [x]. But I do not know how to define join. Cheers, Jan