diff --git a/core/src/main/scala/cats/SemigroupK.scala b/core/src/main/scala/cats/SemigroupK.scala
index c52ad604ab..adfdb3504b 100644
--- a/core/src/main/scala/cats/SemigroupK.scala
+++ b/core/src/main/scala/cats/SemigroupK.scala
@@ -31,9 +31,9 @@ import simulacrum.{op, typeclass}
   /**
    * Compose two SemigroupK intsances.
    */
-  def composedWith[G[_]: SemigroupK]: SemigroupK[λ[α => F[G[α]]]] =
+  def compose[G[_]: SemigroupK]: SemigroupK[λ[α => F[G[α]]]] =
     new SemigroupK[λ[α => F[G[α]]]] {
-      def combine[A](x: F[G[A]], y: F[G[A]]): F[G[A]] = combine(x, y)
+      def combine[A](x: F[G[A]], y: F[G[A]]): F[G[A]] = self.combine(x, y)
     }
 
   /**
diff --git a/tests/src/test/scala/cats/tests/ComposeTests.scala b/tests/src/test/scala/cats/tests/ComposeTests.scala
new file mode 100644
index 0000000000..5aca2b5628
--- /dev/null
+++ b/tests/src/test/scala/cats/tests/ComposeTests.scala
@@ -0,0 +1,58 @@
+package cats
+package tests
+
+import cats.data.{ NonEmptyList, NonEmptyVector, OneAnd }
+import cats.laws.discipline.{ ApplicativeTests, FoldableTests, MonoidalTests, SemigroupKTests, arbitrary, eq }, arbitrary._, eq._
+import org.scalacheck.Arbitrary
+
+class ComposeTests extends CatsSuite {
+  // we have a lot of generated lists of lists in these tests. We have to tell
+  // Scalacheck to calm down a bit so we don't hit memory and test duration
+  // issues.
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    PropertyCheckConfig(maxSize = 5, minSuccessful = 20)
+
+  {
+    // Applicative composition
+
+    implicit val applicativeListVector: Applicative[Lambda[A => List[Vector[A]]]] = Applicative[List] compose Applicative[Vector]
+    implicit val iso = MonoidalTests.Isomorphisms.invariant[Lambda[A => List[Vector[A]]]]
+
+    checkAll("Applicative[Lambda[A => List[Vector[A]]]]", ApplicativeTests[Lambda[A => List[Vector[A]]]].applicative[Int, Int, Int])
+  }
+
+  {
+    // Foldable composition
+
+    implicit val foldableListVector: Foldable[Lambda[A => List[Vector[A]]]] = Foldable[List] compose Foldable[Vector]
+
+    checkAll("Foldable[Lambda[A => List[Vector[A]]]]", FoldableTests[Lambda[A => List[Vector[A]]]].foldable[Int, Int])
+  }
+
+  {
+    // Reducible composition
+
+    val nelReducible =
+      new NonEmptyReducible[NonEmptyList, List] {
+        def split[A](fa: NonEmptyList[A]): (A, List[A]) = (fa.head, fa.tail)
+      }
+
+    val nevReducible =
+      new NonEmptyReducible[NonEmptyVector, Vector] {
+        def split[A](fa: NonEmptyVector[A]): (A, Vector[A]) = (fa.head, fa.tail)
+      }
+
+    implicit val reducibleListVector: Reducible[Lambda[A => NonEmptyList[NonEmptyVector[A]]]] = nelReducible compose nevReducible
+
+    // No Reducible-specific laws, so check the Foldable laws are satisfied
+    checkAll("Reducible[Lambda[A => List[Vector[A]]]]", FoldableTests[Lambda[A => NonEmptyList[NonEmptyVector[A]]]].foldable[Int, Int])
+  }
+
+  {
+    // SemigroupK composition
+
+    implicit val semigroupKListVector: SemigroupK[Lambda[A => List[Vector[A]]]] = SemigroupK[List] compose SemigroupK[Vector]
+
+    checkAll("SemigroupK[Lambda[A => List[Vector[A]]]]", SemigroupKTests[Lambda[A => List[Vector[A]]]].semigroupK[Int])
+  }
+}