bijectionK.scala

type ~>[F[_], G[_]] = [A] => F[A] => G[A]

final case class <~>[F[_], G[_]](to: F ~> G, from: G ~> F):
  val mapAsTo: [A, B] => (G[A] => G[B]) => (F[A] => F[B]) =
    [A, B] => (f: (G[A] => G[B])) => to[A].andThen(f).andThen(from[B])
  val mapAsFrom: [A, B] => (F[A] => F[B]) => (G[A] => G[B]) =
    [A, B] => (f: (F[A] => F[B])) => from[A].andThen(f).andThen(to[B])

extension [F[_], A](fa: F[A])
  transparent inline def mapAs[G[_]]: [B] => (G[A] => G[B]) => F[B] =
    scala.compiletime.summonFrom {
      case biK: (F <~> G) => [B] => (f: (G[A] => G[B])) => biK.mapAsTo[A, B](f)(fa)
      case biK: (G <~> F) => [B] => (f: (G[A] => G[B])) => biK.mapAsFrom[A, B](f)(fa)
    }

// idea: (fa: F[A]).mapAs[G] { ga => g... : G[B] } : F[B]

https://scastie.scala-lang.org/G37skdDnS9maycTAhl5sRw