That doesn't capture the type of the original example. BitSet(1, 2, 3).map { _.toString + "!" } // returns Set[String] The Scala code here starts with one

That doesn't capture the type of the original example. BitSet(1, 2, 3).map { _.toString + "!" } // returns Set[String] The Scala code here starts with one Functor (BitSet) and returns a different Functor (Set), depending on the type of the function (in this case, Int => String). If the function had type (Int => Int), it would still return a BitSet. The signature for fmap does not encode this flexibility.