Yoneda.scala

import cats._

abstract class Yoneda[F[_]: Functor, A] { self =>

  def apply[B](f: A => B): F[B]

  def run: F[A] = apply(identity)

  def map[B](f: A => B): Yoneda[F, B] = new Yoneda[F, B] {
    def apply[C](g: B => C): F[C] = self.apply(f andThen g)
  }
}

def toYoneda[F[_]: Functor, A](fa: F[A]): Yoneda[F, A] =
  new Yoneda[F, A] {
    override def apply[B](f: (A) => B): F[B] = Functor[F].map(fa)(f)
  }

def fromYoneda[F[_], A](y: Yoneda[F, A]): F[A] = y.run