CoproductInject.scala

import cats.data.Coproduct
import cats.free.Inject

object CoproductInject {
  trait A[T]
  trait B[T]
  trait C[T]

  type Two[T] = Coproduct[A, B, T]

  val IA = implicitly[Inject[A, Two]] // Works
  val IB = implicitly[Inject[B, Two]] // Works

  type Three[T] = Coproduct[Two, C, T]

  val IAT = implicitly[Inject[A, Three]] // Doesn't work
  val IBT = implicitly[Inject[B, Three]] // Doesn't work
  val ICT = implicitly[Inject[C, Three]] // Works
}