gistfile1.scala

trait Category[~>[_, _]] {
  def compose[A, B, C](f: B ~> C)(g: A ~> B): A ~> C
  def id[A]: A ~> A
}

case class Lens[A, B](
  get: A => B
, set: (A, B) => A
)

object Category {
  val Function1Category: Category[Function1] = new Category[Function1] {
    def compose[A, B, C](f: B ~> C)(g: A ~> B) = f compose g
    def id[A] = a => a 
  }

  val LensCategory: Category[Lens] =
    sys.error("todo")
}