map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>> map (+1) [1, 2, 3] [2,3,4]
toList (map f xs) = map f (toList xs)
toNonEmpty (map f xs) = map f (toNonEmpty xs)
map id = cat map (g . f) = map f >-> map g