I think it's important to point out that Functor, Applicative, etc. are not only about "containers" like lists and trees which hold a specific set of concrete v

I think it's important to point out that Functor, Applicative, etc. are not only about "containers" like lists and trees which hold a specific set of concrete values but also things like IO actions ("compose this pure function with the result of the readLine action, producing a new action") or even regular functions (where the map operation is just function composition). When other languages import the concept they unfortunately often specialise it to only work on containers.