The last part is backwards -- when F is a functor, the only law we need to check is the identity law, but checking the composition law isn't enough. For example

The last part is backwards -- when F is a functor, the only law we need to check is the identity law, but checking the composition law isn't enough. For example, fmap _ _ = [] satisfies fmap f . fmap g = fmap (f . g), but not fmap id = id.