ProfunctorK just because you can

ProfunctorK.scala

import cats.*

trait Algebra[F[_], G[_]] {
  def apply[A](fa: F[A]): G[A]
}

trait ProfunctorK[Alg[_[_], _[_]]]:
  def lmapK[A[_], B[_], C[_]](s: Alg[A, C])(f: B ~> A): Alg[B, C] =
    dimapK(s)(f)(FunctionK.id)

  def rmapK[A[_], B[_], C[_]](s: Alg[A, C])(g: C ~> D): Alg[A, D] =
    dimapK(s)(FunctionK.id)(g)
    
  def dimapK[A[_], B[_], C[_], D[_]](s: Alg[A, C])(f: B ~> A)(g: C ~> D): Alg[B, D]

object ProfunctorK:
  val algebra: ProfunctorK[Algebra] = new ProfunctorK[Algebra] {
    override def dimapK[A[_], B[_], C[_], D[_]](s: Algebra[A, C])(f: B ~> A)(g: C ~> D): Algebra[B, D] = new Algebra[B, D] {
      override def apply[X](fa: B[X]): D[X] =
        g(s(f(fa)))
    }
  }