IMO after the first section the headings in the post are misleading: - A functor is "not a functor" because not all endofunctors on Hask can be written as Hask

IMO after the first section the headings in the post are misleading: - A functor is "not a functor" because not all endofunctors on Hask can be written as Haskell Functors. - A monad is "not a monad" because you can implement a monad without satisfying all the monad laws. I don't think either of these statements _really_ evidence the claims the headings make. Good post though, I always find that it's useful to think about the subtleties between mathematical objects and their implementation.