[mundacho]

I think the problem here is terminology. A functor is the abstract concept and it implies having the map operation with the right signature and obeying the right properties.

The best way to say it is "The list type 'forms' a functor" or "The Either type 'forms' a functor". The fact that they form a functor implies that their map operation has a fixed set of properties, and these properties are independent of what exactly the data structure does and how it works.