Generalizing the definition of an F-algebra in Scala

gistfile1.scala

/**
 * http://stackoverflow.com/questions/16015020/what-does-coalgebra-mean-in-the-context-of-programming
 **/
def op[T: Monoid](arg: \/[(T, T), T]): T = {
  val m = implicitly[Monoid[T]]
  arg match {
    case -\/((a, b)) => m.append(a, b)
    case \/-(a) => m.zero
  }
}

sealed trait MonoidArgument[+T]
case class Mappend[T](t1: T, t2: T) extends MonoidArgument[T]
case object Mempty extends MonoidArgument[Nothing]

implicit def MonoidArgumentFunctor: Functor[MonoidArgument] = new Functor[MonoidArgument] {
  def map[A, B](a: MonoidArgument[A])(f: A => B): MonoidArgument[B] = a match {
    case Mappend(x, y) => Mappend(f(x), f(y))
    case Mempty => Mempty
  }
}

import scala.language.higherKinds
abstract class Algebra[F[_]: Functor, A] {
  def op: F[A] => A
}