I think the confusion is calling anything that doesn't "obey the rules" a map function just because it is named "map". For example, ruby's hash "map" returns a

I think the confusion is calling anything that doesn't "obey the rules" a map function just because it is named "map". For example, ruby's hash "map" returns an array instead of hash. That's not really a map, is it? Making this useless distinction between "things with map function" and "functors" serves no purpose. It should be "things with real/fake map functions". The name of the function does not matter!