diff --git a/build.sbt b/build.sbt
index b8f0ca2604..9c9122c794 100644
--- a/build.sbt
+++ b/build.sbt
@@ -391,7 +391,11 @@ def mimaSettings(moduleName: String) = Seq(
       exclude[InheritedNewAbstractMethodProblem]("cats.instances.Function1Instances0.catsStdDistributiveForFunction1"),
       exclude[InheritedNewAbstractMethodProblem]("cats.instances.Function1Instances0.catsStdDistributiveForFunction1"),
       exclude[ReversedMissingMethodProblem]("cats.kernel.instances.MapInstances.catsKernelStdCommutativeMonoidForMap"),
-      exclude[IncompatibleResultTypeProblem]("cats.data.KleisliInstances0.catsDataMonadForKleisliId")
+      exclude[IncompatibleResultTypeProblem]("cats.data.KleisliInstances0.catsDataMonadForKleisliId"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.kernel.PartialOrderToPartialOrderingConversion.catsKernelPartialOrderingForPartialOrder"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.kernel.EqToEquivConversion.catsKernelEquivForEq"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.kernel.OrderToOrderingConversion.catsKernelOrderingForOrder"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.kernel.HashToHashingConversion.catsKernelHashToHashing")
     )
   }
 )
diff --git a/core/src/main/scala/cats/instances/eq.scala b/core/src/main/scala/cats/instances/eq.scala
index dc304686d5..364c1962d7 100644
--- a/core/src/main/scala/cats/instances/eq.scala
+++ b/core/src/main/scala/cats/instances/eq.scala
@@ -1,7 +1,7 @@
 package cats
 package instances
 
-trait EqInstances {
+trait EqInstances extends kernel.instances.EqInstances {
   implicit val catsContravariantMonoidalForEq: ContravariantMonoidal[Eq] =
     new ContravariantMonoidal[Eq] {
       /**
diff --git a/core/src/main/scala/cats/instances/hash.scala b/core/src/main/scala/cats/instances/hash.scala
index 443ef96e39..2401313148 100644
--- a/core/src/main/scala/cats/instances/hash.scala
+++ b/core/src/main/scala/cats/instances/hash.scala
@@ -2,7 +2,7 @@ package cats
 package instances
 
 
-trait HashInstances {
+trait HashInstances extends kernel.instances.HashInstances {
 
   implicit val catsContravariantForHash: Contravariant[Hash] =
     new Contravariant[Hash] {
diff --git a/core/src/main/scala/cats/instances/order.scala b/core/src/main/scala/cats/instances/order.scala
index 8a239d264c..1e44c3f932 100644
--- a/core/src/main/scala/cats/instances/order.scala
+++ b/core/src/main/scala/cats/instances/order.scala
@@ -1,7 +1,7 @@
 package cats
 package instances
 
-trait OrderInstances extends cats.kernel.OrderToOrderingConversion {
+trait OrderInstances extends kernel.instances.OrderInstances {
   implicit val catsContravariantMonoidalForOrder: ContravariantMonoidal[Order] =
     new ContravariantMonoidal[Order] {
       /**
diff --git a/core/src/main/scala/cats/instances/partialOrder.scala b/core/src/main/scala/cats/instances/partialOrder.scala
index 671e0b82cf..cfdab8db32 100644
--- a/core/src/main/scala/cats/instances/partialOrder.scala
+++ b/core/src/main/scala/cats/instances/partialOrder.scala
@@ -1,7 +1,7 @@
 package cats
 package instances
 
-trait PartialOrderInstances {
+trait PartialOrderInstances extends kernel.instances.PartialOrderInstances {
   implicit val catsContravariantSemigroupalForPartialOrder: ContravariantSemigroupal[PartialOrder] =
     new ContravariantSemigroupal[PartialOrder] {
       /** Derive a `PartialOrder` for `B` given a `PartialOrder[A]` and a function `B => A`.
diff --git a/kernel-laws/src/test/scala/cats/kernel/laws/LawTests.scala b/kernel-laws/src/test/scala/cats/kernel/laws/LawTests.scala
index 94aec53ea3..b5cf16a036 100644
--- a/kernel-laws/src/test/scala/cats/kernel/laws/LawTests.scala
+++ b/kernel-laws/src/test/scala/cats/kernel/laws/LawTests.scala
@@ -243,6 +243,21 @@ class Tests extends FunSuite with Discipline {
 
   checkAll("subsetPartialOrder[Int]", PartialOrderTests(subsetPartialOrder[Int]).partialOrder)
 
+  {
+    implicit def subsetPartialOrdering[A]: PartialOrdering[Set[A]] = new PartialOrdering[Set[A]] {
+
+      override def tryCompare(x: Set[A], y: Set[A]): Option[Int] = {
+        if (x == y) Some(0)
+        else if (x subsetOf y) Some(-1)
+        else if (y subsetOf x) Some(1)
+        else None
+      }
+
+      override def lteq(x: Set[A], y: Set[A]): Boolean = (x subsetOf y) || (x == y)
+    }
+    checkAll("fromPartialOrdering[Int]", PartialOrderTests(PartialOrder.fromPartialOrdering[Set[Int]]).partialOrder)
+  }
+
   implicit val arbitraryComparison: Arbitrary[Comparison] =
     Arbitrary(Gen.oneOf(Comparison.GreaterThan, Comparison.EqualTo, Comparison.LessThan))
 
diff --git a/kernel/src/main/scala/cats/kernel/Eq.scala b/kernel/src/main/scala/cats/kernel/Eq.scala
index 227937c632..9caf1c0700 100644
--- a/kernel/src/main/scala/cats/kernel/Eq.scala
+++ b/kernel/src/main/scala/cats/kernel/Eq.scala
@@ -32,7 +32,17 @@ abstract class EqFunctions[E[T] <: Eq[T]] {
 
 }
 
-object Eq extends EqFunctions[Eq] {
+trait EqToEquivConversion {
+  /**
+   * Implicitly derive a `scala.math.Equiv[A]` from a `Eq[A]`
+   * instance.
+   */
+  implicit def catsKernelEquivForEq[A](implicit ev: Eq[A]): Equiv[A] = new Equiv[A] {
+    def equiv(a: A, b: A) = ev.eqv(a, b)
+  }
+}
+
+object Eq extends EqFunctions[Eq] with EqToEquivConversion {
 
   /**
    * Access an implicit `Eq[A]`.
@@ -66,13 +76,6 @@ object Eq extends EqFunctions[Eq] {
       def eqv(x: A, y: A) = eq1.eqv(x, y) || eq2.eqv(x, y)
     }
 
-  /**
-   * This gives compatibility with scala's Equiv trait
-   */
-  implicit def catsKernelEquivForEq[A](implicit ev: Eq[A]): Equiv[A] =
-    new Equiv[A] {
-      def equiv(a: A, b: A) = ev.eqv(a, b)
-    }
 
   /**
    * Create an `Eq` instance from an `eqv` implementation.
diff --git a/kernel/src/main/scala/cats/kernel/Hash.scala b/kernel/src/main/scala/cats/kernel/Hash.scala
index ef8e88d742..4579f12184 100644
--- a/kernel/src/main/scala/cats/kernel/Hash.scala
+++ b/kernel/src/main/scala/cats/kernel/Hash.scala
@@ -54,3 +54,9 @@ object Hash extends HashFunctions[Hash] {
     }
 
 }
+
+trait HashToHashingConversion {
+  implicit def catsKernelHashToHashing[A](implicit ev: Hash[A]): Hashing[A] = new Hashing[A] {
+    override def hash(x: A): Int = ev.hash(x)
+  }
+}
diff --git a/kernel/src/main/scala/cats/kernel/Order.scala b/kernel/src/main/scala/cats/kernel/Order.scala
index 2b580cd142..4ddff806d6 100644
--- a/kernel/src/main/scala/cats/kernel/Order.scala
+++ b/kernel/src/main/scala/cats/kernel/Order.scala
@@ -115,9 +115,10 @@ trait OrderToOrderingConversion {
    */
   implicit def catsKernelOrderingForOrder[A](implicit ev: Order[A]): Ordering[A] =
     ev.toOrdering
+
 }
 
-object Order extends OrderFunctions[Order] {
+object Order extends OrderFunctions[Order] with OrderToOrderingConversion {
   /**
    * Access an implicit `Order[A]`.
    */
@@ -164,13 +165,6 @@ object Order extends OrderFunctions[Order] {
       def compare(x: A, y: A) = f(x, y)
     }
 
-  /**
-   * Implicitly convert a `Order[A]` to a `scala.math.Ordering[A]`
-   * instance.
-   */
-  implicit def catsKernelOrderingForOrder[A](implicit ev: Order[A]): Ordering[A] =
-    ev.toOrdering
-
   /**
    * An `Order` instance that considers all `A` instances to be equal.
    */
diff --git a/kernel/src/main/scala/cats/kernel/PartialOrder.scala b/kernel/src/main/scala/cats/kernel/PartialOrder.scala
index 048041b0f1..caa3baf535 100644
--- a/kernel/src/main/scala/cats/kernel/PartialOrder.scala
+++ b/kernel/src/main/scala/cats/kernel/PartialOrder.scala
@@ -123,7 +123,7 @@ abstract class PartialOrderFunctions[P[T] <: PartialOrder[T]] extends EqFunction
     ev.gt(x, y)
 }
 
-object PartialOrder extends PartialOrderFunctions[PartialOrder] {
+object PartialOrder extends PartialOrderFunctions[PartialOrder] with PartialOrderToPartialOrderingConversion {
   /**
    * Access an implicit `PartialOrder[A]`.
    */
@@ -154,10 +154,14 @@ object PartialOrder extends PartialOrderFunctions[PartialOrder] {
       def partialCompare(x: A, y: A) = f(x, y)
     }
 
-  /**
-   * Implicitly convert a `PartialOrder[A]` to a
-   * `scala.math.PartialOrdering[A]` instance.
-   */
+  def fromPartialOrdering[A](implicit ev: PartialOrdering[A]): PartialOrder[A] = new PartialOrder[A] {
+    def partialCompare(x: A, y: A): Double =
+      ev.tryCompare(x, y).fold(Double.NaN)(_.toDouble)
+  }
+}
+
+
+trait PartialOrderToPartialOrderingConversion {
   implicit def catsKernelPartialOrderingForPartialOrder[A](implicit ev: PartialOrder[A]): PartialOrdering[A] =
     new PartialOrdering[A] {
       def tryCompare(x: A, y: A): Option[Int] = ev.tryCompare(x, y)
diff --git a/kernel/src/main/scala/cats/kernel/instances/all.scala b/kernel/src/main/scala/cats/kernel/instances/all.scala
index 954431c68a..1af2f0b0da 100644
--- a/kernel/src/main/scala/cats/kernel/instances/all.scala
+++ b/kernel/src/main/scala/cats/kernel/instances/all.scala
@@ -11,15 +11,19 @@ trait AllInstances
     with ByteInstances
     with CharInstances
     with DoubleInstances
+    with EqInstances
     with EitherInstances
     with DurationInstances
     with FloatInstances
     with FunctionInstances
+    with HashInstances
     with IntInstances
     with ListInstances
     with LongInstances
     with MapInstances
     with OptionInstances
+    with OrderInstances
+    with PartialOrderInstances
     with QueueInstances
     with SetInstances
     with ShortInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/eq.scala b/kernel/src/main/scala/cats/kernel/instances/eq.scala
new file mode 100644
index 0000000000..2ffbf559ad
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/eq.scala
@@ -0,0 +1,6 @@
+package cats.kernel
+package instances
+
+trait EqInstances extends EqToEquivConversion
+
+object eq extends EqInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/hash.scala b/kernel/src/main/scala/cats/kernel/instances/hash.scala
new file mode 100644
index 0000000000..3822096596
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/hash.scala
@@ -0,0 +1,6 @@
+package cats.kernel
+package instances
+
+trait HashInstances extends HashToHashingConversion
+
+object hash extends HashInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/order.scala b/kernel/src/main/scala/cats/kernel/instances/order.scala
new file mode 100644
index 0000000000..e678dc34d9
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/order.scala
@@ -0,0 +1,6 @@
+package cats.kernel
+package instances
+
+trait OrderInstances extends OrderToOrderingConversion
+
+object order extends OrderInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/partialOrder.scala b/kernel/src/main/scala/cats/kernel/instances/partialOrder.scala
new file mode 100644
index 0000000000..b7dfc5819b
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/partialOrder.scala
@@ -0,0 +1,6 @@
+package cats.kernel
+package instances
+
+trait PartialOrderInstances extends PartialOrderToPartialOrderingConversion
+
+object partialOrder extends PartialOrderInstances