One can map over a list of lists of arbitrary depth as follows:

map           :: (a -> b) ->   [a]   ->   [b]
(map.map)     :: (a -> b) ->  [[a]]  ->  [[b]]
(map.map.map) :: (a -> b) -> [[[a]]] -> [[[b]]]

Is it possible to write a single function handling all such cases? Uiua has the ∵ each function which does this on an array of arbitrary rank. Such functions are called pervasive functions in array languages.