How to create a generic Monoid from an ADT

Question

Given I have an existing ADT, is it possible to create a generic monoid.

From now, I have as many monoid as classes in my ADT, but it's not DRY.

Here is the code :

import scalaz._
import Scalaz._

object DataRework extends App {
  sealed trait MultiItemValue {
    type MV
    def value: Seq[MV]
  }

  case class StringValue(value: Seq[String]) extends MultiItemValue{type MV = String}
  case class BooleanValue(value: Seq[Boolean]) extends MultiItemValue{type MV = Boolean}

  implicit object BooleanValueMonoid extends Monoid[BooleanValue] {
    override def zero: BooleanValue = BooleanValue(Nil)
    override def append(f1: BooleanValue, f2: => BooleanValue): BooleanValue = BooleanValue(f1.value ++ f2.value)
  }

  implicit object StringValueMonoid extends Monoid[StringValue] {
    override def zero: StringValue = StringValue(Nil)
    override def append(f1: StringValue, f2: => StringValue): StringValue = StringValue(f1.value ++ f2.value)
  }

I would like something like, but i found this code ugly due to some repetition :

  implicit object GenericMonoid extends Monoid[MultiItemValue] {
    override def zero: MultiItemValue = ???
    override def append(f1: MultiItemValue, f2: => MultiItemValue): MultiItemValue = (f1, f2) match {
      case (sv1: StringValue, sv2: StringValue) => StringValue(sv1.value ++ sv2.value)
      case (bv1: BooleanValue, bv2: BooleanValue) => BooleanValue(bv1.value ++ bv2.value)
    }
  }