[chousuke]

"Either" actually isn't a Functor, at least in Haskell

In Haskell, a Functor actually consists of two parts: The type itself (f), which 'transforms' a type a into type "f a". ie. Maybe "applied" to Int gives "Maybe Int", a new simple type (let's handwave kinds away for now). In addition to that, the fmap function is required for Maybe to be a Functor. A Functor is defined by this ability to "add structure" to existing types and the mapping operation.

Seen this way, Either is clearly not a Functor: "Either Int" is not a simple type. However, "Either Int" is a functor: Either Int String forms a simple type, and you can implement fmap. In fact, that works for any type, so "Either a" is the functor as usually defined in Haskell.