diff --git a/core/shared/src/main/scala/zio/prelude/AssociativeBoth.scala b/core/shared/src/main/scala/zio/prelude/AssociativeBoth.scala
index 093f7c060..77d4f32a0 100644
--- a/core/shared/src/main/scala/zio/prelude/AssociativeBoth.scala
+++ b/core/shared/src/main/scala/zio/prelude/AssociativeBoth.scala
@@ -2,7 +2,7 @@ package zio.prelude
 
 import zio._
 import zio.prelude.coherent.AssociativeBothDeriveEqualInvariant
-import zio.prelude.newtypes.{ AndF, Failure, OrF }
+import zio.prelude.newtypes.{ AndF, Failure, Nested, OrF }
 import zio.stm.ZSTM
 import zio.stream.{ ZSink, ZStream }
 import zio.test.TestResult
@@ -1124,6 +1124,18 @@ object AssociativeBoth extends LawfulF.Invariant[AssociativeBothDeriveEqualInvar
         Id(Id.unwrap(fa) -> Id.unwrap(fb))
     }
 
+  implicit def NestedIdentityBoth[F[+_]: IdentityBoth: Covariant, G[+_]](implicit
+    G: IdentityBoth[G]
+  ): IdentityBoth[({ type lambda[+A] = Nested[F, G, A] })#lambda] =
+    new IdentityBoth[({ type lambda[+A] = Nested[F, G, A] })#lambda] {
+      override def any: Nested[F, G, Any] = Nested(G.any.succeed[F])
+
+      override def both[A, B](fa: => Nested[F, G, A], fb: => Nested[F, G, B]): Nested[F, G, (A, B)] =
+        Nested {
+          Nested.unwrap[F[G[A]]](fa).zipWith(Nested.unwrap[F[G[B]]](fb))(_ zip _)
+        }
+    }
+
   /**
    * The `IdentityBoth` (and `AssociativeBoth`) instance for `List`.
    */
diff --git a/core/shared/src/main/scala/zio/prelude/Covariant.scala b/core/shared/src/main/scala/zio/prelude/Covariant.scala
index 064b6a8e8..dbde2b48f 100644
--- a/core/shared/src/main/scala/zio/prelude/Covariant.scala
+++ b/core/shared/src/main/scala/zio/prelude/Covariant.scala
@@ -1,6 +1,7 @@
 package zio.prelude
 
 import zio.prelude.coherent.CovariantDeriveEqual
+import zio.prelude.newtypes.{ Nested }
 import zio.test.TestResult
 import zio.test.laws._
 
@@ -95,6 +96,18 @@ object Covariant extends LawfulF.Covariant[CovariantDeriveEqual, Equal] {
   def apply[F[+_]](implicit covariant: Covariant[F]): Covariant[F] =
     covariant
 
+  implicit def NestedCovariant[F[+_], G[+_]](implicit
+    F: Covariant[F],
+    G: Covariant[G]
+  ): Covariant[({ type lambda[+A] = Nested[F, G, A] })#lambda] =
+    new Covariant[({ type lambda[+A] = Nested[F, G, A] })#lambda] {
+      private lazy val composedCovariant = F.compose(G)
+
+      override def map[A, B](f: A => B): Nested[F, G, A] => Nested[F, G, B] = { x: Nested[F, G, A] =>
+        Nested(composedCovariant.map(f)(Nested.unwrap[F[G[A]]](x)))
+      }
+    }
+
 }
 
 trait CovariantSyntax {
diff --git a/core/shared/src/main/scala/zio/prelude/Derive.scala b/core/shared/src/main/scala/zio/prelude/Derive.scala
index 33292901f..f94effd84 100644
--- a/core/shared/src/main/scala/zio/prelude/Derive.scala
+++ b/core/shared/src/main/scala/zio/prelude/Derive.scala
@@ -1,5 +1,6 @@
 package zio.prelude
 
+import zio.prelude.newtypes.Nested
 import zio.{ Cause, Chunk, Exit, NonEmptyChunk }
 
 import scala.util.Try
@@ -31,6 +32,26 @@ object Derive {
   def apply[F[_], Typeclass[_]](implicit derive: Derive[F, Typeclass]): Derive[F, Typeclass] =
     derive
 
+  /**
+   * The `DeriveEqual` instance for `Id`.
+   */
+  implicit val IdDeriveEqual: Derive[Id, Equal] =
+    new Derive[Id, Equal] {
+      override def derive[A: Equal]: Equal[Id[A]] = Id.wrapAll(Equal[A])
+    }
+
+  /**
+   * The `DeriveEqual` instance for `Nested`.
+   */
+  implicit def NestedDeriveEqual[F[+_], G[+_]](implicit
+    F: Derive[F, Equal],
+    G: Derive[G, Equal]
+  ): Derive[({ type lambda[A] = Nested[F, G, A] })#lambda, Equal] =
+    new Derive[({ type lambda[A] = Nested[F, G, A] })#lambda, Equal] {
+      override def derive[A: Equal]: Equal[Nested[F, G, A]] =
+        Equal.NestedEqual(F.derive(G.derive[A]))
+    }
+
   /**
    * The `DeriveEqual` instance for `Chunk`.
    */
diff --git a/core/shared/src/main/scala/zio/prelude/Equal.scala b/core/shared/src/main/scala/zio/prelude/Equal.scala
index cbafa3187..a9d7c00c5 100644
--- a/core/shared/src/main/scala/zio/prelude/Equal.scala
+++ b/core/shared/src/main/scala/zio/prelude/Equal.scala
@@ -2,6 +2,7 @@ package zio.prelude
 
 import zio.Exit.{ Failure, Success }
 import zio.prelude.coherent.HashOrd
+import zio.prelude.newtypes.Nested
 import zio.test.TestResult
 import zio.test.laws.{ Lawful, Laws }
 import zio.{ Cause, Chunk, Exit, Fiber, NonEmptyChunk, ZTrace }
@@ -204,6 +205,17 @@ object Equal extends Lawful[Equal] {
   def default[A]: Equal[A] =
     make(_ == _)
 
+  implicit def IdEqual[A: Equal]: Equal[Id[A]] = new Equal[Id[A]] {
+    override protected def checkEqual(l: Id[A], r: Id[A]): Boolean =
+      Id.unwrap[A](l) === Id.unwrap[A](r)
+  }
+
+  implicit def NestedEqual[F[+_], G[+_], A](implicit eqFGA: Equal[F[G[A]]]): Equal[Nested[F, G, A]] =
+    new Equal[Nested[F, G, A]] {
+      override protected def checkEqual(l: Nested[F, G, A], r: Nested[F, G, A]): Boolean =
+        eqFGA.checkEqual(Nested.unwrap[F[G[A]]](l), Nested.unwrap[F[G[A]]](r))
+    }
+
   /**
    * `Hash` and `Ord` (and thus also `Equal`) instance for `Boolean` values.
    */
diff --git a/core/shared/src/main/scala/zio/prelude/GenFs.scala b/core/shared/src/main/scala/zio/prelude/GenFs.scala
index db0d34677..cd0a48229 100644
--- a/core/shared/src/main/scala/zio/prelude/GenFs.scala
+++ b/core/shared/src/main/scala/zio/prelude/GenFs.scala
@@ -1,6 +1,6 @@
 package zio.prelude
 
-import zio.prelude.newtypes.Failure
+import zio.prelude.newtypes.{ Failure, Nested }
 import zio.random.Random
 import zio.test.Gen.oneOf
 import zio.test._
@@ -109,4 +109,17 @@ object GenFs {
       def apply[R1 <: R, E](e: Gen[R1, E]): Gen[R1, Failure[Validation[E, A]]] =
         Gens.validation(e, a).map(Failure.wrap)
     }
+
+  def nested[F[+_], G[+_], RF, RG](
+    genF: GenF[RF, F],
+    genG: GenF[RG, G]
+  ): GenF[RF with RG, ({ type lambda[+A] = Nested[F, G, A] })#lambda] =
+    new GenF[RF with RG, ({ type lambda[+A] = Nested[F, G, A] })#lambda] {
+      override def apply[R1 <: RF with RG, A](gen: Gen[R1, A]): Gen[R1, Nested[F, G, A]] = {
+        val value: Gen[R1 with RG with RF, newtypes.Nested.newtypeF.Type[F[G[A]]]] =
+          genF(genG(gen)).map(Nested(_): Nested[F, G, A])
+        value
+      }
+
+    }
 }
diff --git a/core/shared/src/main/scala/zio/prelude/Invariant.scala b/core/shared/src/main/scala/zio/prelude/Invariant.scala
index 3334709d0..9004a64f0 100644
--- a/core/shared/src/main/scala/zio/prelude/Invariant.scala
+++ b/core/shared/src/main/scala/zio/prelude/Invariant.scala
@@ -677,6 +677,8 @@ object Invariant extends LowPriorityInvariantImplicits with InvariantVersionSpec
     new Traversable[Option] {
       def foreach[G[+_]: IdentityBoth: Covariant, A, B](option: Option[A])(f: A => G[B]): G[Option[B]] =
         option.fold[G[Option[B]]](Option.empty.succeed)(a => f(a).map(Some(_)))
+
+      override def map[A, B](f: A => B): Option[A] => Option[B] = _.map(f)
     }
 
   /**
diff --git a/core/shared/src/main/scala/zio/prelude/Traversable.scala b/core/shared/src/main/scala/zio/prelude/Traversable.scala
index 0474ab985..4792e4094 100644
--- a/core/shared/src/main/scala/zio/prelude/Traversable.scala
+++ b/core/shared/src/main/scala/zio/prelude/Traversable.scala
@@ -1,7 +1,8 @@
 package zio.prelude
 
 import zio.prelude.coherent.DeriveEqualTraversable
-import zio.prelude.newtypes.{ And, First, Max, Min, Or, Prod, Sum }
+import zio.prelude.newtypes._
+import zio.test.TestResult
 import zio.test.laws._
 import zio.{ Chunk, ChunkBuilder, NonEmptyChunk }
 
@@ -269,17 +270,68 @@ trait Traversable[F[+_]] extends Covariant[F] {
 
 object Traversable extends LawfulF.Covariant[DeriveEqualTraversable, Equal] {
 
+  /**
+   * Identity Law :
+   *  traverse Identity ta = Identity ta
+   */
+  val traversableIdentityLaw: LawsF.Covariant[DeriveEqualTraversable, Equal] =
+    new LawsF.Covariant.Law1[DeriveEqualTraversable, Equal]("traversableIdentityLaw") {
+      def apply[F[+_]: DeriveEqualTraversable, A: Equal](fa: F[A]): TestResult =
+        fa.foreach(Id(_)) <-> Id(fa)
+    }
+
+  /**
+   *  Composition Law for various kind of Applivatives
+   */
+  val traversableCompositionLaw: LawsF.Covariant[DeriveEqualTraversable, Equal] = {
+    compositionLawCase[Id, Id] + compositionLawCase[Option, List] + compositionLawCase[List, Option]
+  }
+
+  /**
+   * Composition law
+   * traverse (Compose . fmap g . f) ta = Compose . fmap (traverse g) . traverse f $ ta
+   */
+  private def compositionLawCase[F[+_]: IdentityBoth: Covariant: DeriveEqual, G[
+    +_
+  ]: IdentityBoth: Covariant: DeriveEqual]: LawsF.Covariant[DeriveEqualTraversable, Equal] =
+    new LawsF.Covariant.ComposeLaw[DeriveEqualTraversable, Equal]("traversableCompositionLaw") {
+      def apply[T[+_]: DeriveEqualTraversable, A: Equal, B: Equal, C: Equal](
+        ta: T[A],
+        f: A => B,
+        g: B => C
+      ): TestResult = {
+        val fA: A => F[B]             = f.map(_.succeed[F])
+        val gA: B => G[C]             = g.map(_.succeed[G])
+        val left: Nested[F, G, T[C]]  = Nested(ta.foreach(fA).map(_.foreach(gA)))
+        val right: Nested[F, G, T[C]] = ta.foreach(a => Nested(fA(a).map(gA)): Nested[F, G, C])
+        left <-> right
+      }
+    }
+
   /**
    * The set of all laws that instances of `Traversable` must satisfy.
    */
   val laws: LawsF.Covariant[DeriveEqualTraversable, Equal] =
-    Covariant.laws
+    traversableIdentityLaw + traversableCompositionLaw + Covariant.laws
 
   /**
    * Summons an implicit `Traversable`.
    */
   def apply[F[+_]](implicit traversable: Traversable[F]): Traversable[F] =
     traversable
+
+  implicit def NestedTraversable[F[+_]: Traversable, G[+_]: Traversable]
+    : Traversable[({ type lambda[+A] = Nested[F, G, A] })#lambda] =
+    new Traversable[({ type lambda[+A] = Nested[F, G, A] })#lambda] {
+      override def foreach[E[+_]: IdentityBoth: Covariant, A, B](ta: Nested[F, G, A])(
+        f: A => E[B]
+      ): E[Nested[F, G, B]] =
+        Nested.wrapAll(Nested.unwrap[F[G[A]]](ta).foreach(_.foreach(f)))
+
+      private lazy val nestedCovariant = Covariant.NestedCovariant[F, G]
+
+      override def map[A, B](f: A => B): Nested[F, G, A] => Nested[F, G, B] = nestedCovariant.map(f)
+    }
 }
 
 trait TraversableSyntax {
diff --git a/core/shared/src/main/scala/zio/prelude/coherent/coherent.scala b/core/shared/src/main/scala/zio/prelude/coherent/coherent.scala
index 59d46eda1..b9e917f62 100644
--- a/core/shared/src/main/scala/zio/prelude/coherent/coherent.scala
+++ b/core/shared/src/main/scala/zio/prelude/coherent/coherent.scala
@@ -210,6 +210,11 @@ object DeriveEqualTraversable {
         deriveEqual0.derive
       def foreach[G[+_]: IdentityBoth: Covariant, A, B](fa: F[A])(f: A => G[B]): G[F[B]] =
         traversable0.foreach(fa)(f)
+
+      // Traversable provides default implementation for Covariant.map,
+      // so if we want properly check Covariant laws for Traversable instance with overrode 'map'
+      // we need to forward it
+      override def map[A, B](f: A => B): F[A] => F[B] = traversable0.map(f)
     }
 }
 
diff --git a/core/shared/src/main/scala/zio/prelude/newtypes/package.scala b/core/shared/src/main/scala/zio/prelude/newtypes/package.scala
index e78ad61ee..5526efcf4 100644
--- a/core/shared/src/main/scala/zio/prelude/newtypes/package.scala
+++ b/core/shared/src/main/scala/zio/prelude/newtypes/package.scala
@@ -91,4 +91,14 @@ package object newtypes {
   object FailureOut extends NewtypeF
 
   type FailureOut[+A] = FailureOut.Type[A]
+
+  /**
+   * A newtype representing Right-to-left composition of functors.
+   * If F[_] and G[_] are both Covariant, then Nested[F, G, *] is also a Covariant
+   * If F[_] and G[_] are both IdentityBoth, then Nested[F, G, *] is also an IdentityBoth
+   * If F[_] and G[_] are both Traversable, then Nested[F, G, *] is also a Traversable
+   */
+  object Nested extends NewtypeF
+
+  type Nested[F[+_], G[+_], +A] = Nested.Type[F[G[A]]]
 }
diff --git a/core/shared/src/test/scala/zio/prelude/CovariantSpec.scala b/core/shared/src/test/scala/zio/prelude/CovariantSpec.scala
index b82b72483..e28041e6c 100644
--- a/core/shared/src/test/scala/zio/prelude/CovariantSpec.scala
+++ b/core/shared/src/test/scala/zio/prelude/CovariantSpec.scala
@@ -18,7 +18,8 @@ object CovariantSpec extends DefaultRunnableSpec {
         testM("cause")(checkAllLaws(Covariant)(GenFs.cause, Gen.anyInt)),
         testM("chunk")(checkAllLaws(Covariant)(GenF.chunk, Gen.anyInt)),
         testM("exit")(checkAllLaws(Covariant)(GenFs.exit(Gen.causes(Gen.anyInt, Gen.throwable)), Gen.anyInt)),
-        testM("nonEmptyChunk")(checkAllLaws(Covariant)(GenFs.nonEmptyChunk, Gen.anyInt))
+        testM("nonEmptyChunk")(checkAllLaws(Covariant)(GenFs.nonEmptyChunk, Gen.anyInt)),
+        testM("Nested[vector,cause]")(checkAllLaws(Covariant)(GenFs.nested(GenF.vector, GenFs.cause), Gen.anyInt))
       )
     )
 }
diff --git a/core/shared/src/test/scala/zio/prelude/IdentityBothSpec.scala b/core/shared/src/test/scala/zio/prelude/IdentityBothSpec.scala
index 00f8332ae..7578c1f54 100644
--- a/core/shared/src/test/scala/zio/prelude/IdentityBothSpec.scala
+++ b/core/shared/src/test/scala/zio/prelude/IdentityBothSpec.scala
@@ -1,7 +1,7 @@
 package zio.prelude
 
-import zio.test._
 import zio.test.laws._
+import zio.test.{ testM, _ }
 
 object IdentityBothSpec extends DefaultRunnableSpec {
 
@@ -11,7 +11,10 @@ object IdentityBothSpec extends DefaultRunnableSpec {
         testM("either")(checkAllLaws(IdentityBoth)(GenF.either(Gen.anyInt), Gen.anyInt)),
         testM("list")(checkAllLaws(IdentityBoth)(GenF.list, Gen.anyInt)),
         testM("option")(checkAllLaws(IdentityBoth)(GenF.option, Gen.anyInt)),
-        testM("try")(checkAllLaws(IdentityBoth)(GenFs.tryScala, Gen.anyInt))
+        testM("try")(checkAllLaws(IdentityBoth)(GenFs.tryScala, Gen.anyInt)), {
+          implicit val invariant = Covariant.NestedCovariant[List, Option]
+          testM("Nested[list,option]")(checkAllLaws(IdentityBoth)(GenFs.nested(GenF.list, GenF.option), Gen.anyInt))
+        }
       )
     )
 }
diff --git a/core/shared/src/test/scala/zio/prelude/TraversableSpec.scala b/core/shared/src/test/scala/zio/prelude/TraversableSpec.scala
index 46e27f2a1..c03e01b03 100644
--- a/core/shared/src/test/scala/zio/prelude/TraversableSpec.scala
+++ b/core/shared/src/test/scala/zio/prelude/TraversableSpec.scala
@@ -1,8 +1,8 @@
 package zio.prelude
 
 import zio.random.Random
-import zio.test._
 import zio.test.laws._
+import zio.test.{ Sized, testM, _ }
 import zio.{ Chunk, NonEmptyChunk }
 
 object TraversableSpec extends DefaultRunnableSpec {
@@ -39,7 +39,8 @@ object TraversableSpec extends DefaultRunnableSpec {
         testM("list")(checkAllLaws(Traversable)(GenF.list, Gen.anyInt)),
         testM("map")(checkAllLaws(Traversable)(GenFs.map(Gen.anyInt), Gen.anyInt)),
         testM("option")(checkAllLaws(Traversable)(GenF.option, Gen.anyInt)),
-        testM("vector")(checkAllLaws(Traversable)(GenF.vector, Gen.anyInt))
+        testM("vector")(checkAllLaws(Traversable)(GenF.vector, Gen.anyInt)),
+        testM("Nested[vector,option]")(checkAllLaws(Traversable)(GenFs.nested(GenF.vector, GenF.option), Gen.anyInt))
       ),
       suite("combinators")(
         testM("contains") {