diff --git a/build.sbt b/build.sbt
index fd23f9de69..c4b4cc60f0 100644
--- a/build.sbt
+++ b/build.sbt
@@ -207,7 +207,7 @@ lazy val kernel = crossProject.crossType(CrossType.Pure)
   .settings(scoverageSettings: _*)
   .settings(sourceGenerators in Compile <+= (sourceManaged in Compile).map(KernelBoiler.gen))
   .jsSettings(commonJsSettings:_*)
-  .jvmSettings((commonJvmSettings ++ (mimaPreviousArtifacts := Set("org.typelevel" %% "cats-kernel" % "0.6.0"))):_*)
+  .jvmSettings((commonJvmSettings ++ (mimaPreviousArtifacts := Set("org.typelevel" %% "cats-kernel" % "0.7.0"))):_*)
 
 lazy val kernelJVM = kernel.jvm
 lazy val kernelJS = kernel.js
diff --git a/kernel-laws/src/main/scala/cats/kernel/laws/OrderLaws.scala b/kernel-laws/src/main/scala/cats/kernel/laws/OrderLaws.scala
index 22c47cab7e..27f7f59958 100644
--- a/kernel-laws/src/main/scala/cats/kernel/laws/OrderLaws.scala
+++ b/kernel-laws/src/main/scala/cats/kernel/laws/OrderLaws.scala
@@ -6,7 +6,7 @@ import org.typelevel.discipline.Laws
 import org.scalacheck.{Arbitrary, Prop}
 import org.scalacheck.Prop._
 
-import cats.kernel.instances.boolean._
+import cats.kernel.instances.all._
 
 object OrderLaws {
   def apply[A: Eq: Arbitrary]: OrderLaws[A] = new OrderLaws[A] {
@@ -59,6 +59,26 @@ trait OrderLaws[A] extends Laws {
     },
     "gt" -> forAll { (x: A, y: A) =>
       A.lt(x, y) ?== A.gt(y, x)
+    },
+    "partialCompare" -> forAll { (x: A, y: A) =>
+      val c = A.partialCompare(x, y)
+      ((c < 0) ?== A.lt(x, y)) && ((c == 0) ?== A.eqv(x, y)) && ((c > 0) ?== A.gt(x, y))
+    },
+    "pmin" -> forAll { (x: A, y: A) =>
+      val c = A.partialCompare(x, y)
+      val m = A.pmin(x, y)
+      if (c < 0) m ?== Some(x)
+      else if (c == 0) (m ?== Some(x)) && (m ?== Some(y))
+      else if (c > 0) m ?== Some(y)
+      else m ?== None
+    },
+    "pmax" -> forAll { (x: A, y: A) =>
+      val c = A.partialCompare(x, y)
+      val m = A.pmax(x, y)
+      if (c < 0) m ?== Some(y)
+      else if (c == 0) (m ?== Some(x)) && (m ?== Some(y))
+      else if (c > 0) m ?== Some(x)
+      else m ?== None
     }
   )
 
@@ -67,6 +87,24 @@ trait OrderLaws[A] extends Laws {
     parent = Some(partialOrder),
     "totality" -> forAll { (x: A, y: A) =>
       A.lteqv(x, y) ?|| A.lteqv(y, x)
+    },
+    "compare" -> forAll { (x: A, y: A) =>
+      val c = A.compare(x, y)
+      ((c < 0) ?== A.lt(x, y)) && ((c == 0) ?== A.eqv(x, y)) && ((c > 0) ?== A.gt(x, y))
+    },
+    "min" -> forAll { (x: A, y: A) =>
+      val c = A.compare(x, y)
+      val m = A.min(x, y)
+      if (c < 0) m ?== x
+      else if (c == 0) (m ?== x) && (m ?== y)
+      else m ?== y
+    },
+    "max" -> forAll { (x: A, y: A) =>
+      val c = A.compare(x, y)
+      val m = A.max(x, y)
+      if (c < 0) m ?== y
+      else if (c == 0) (m ?== x) && (m ?== y)
+      else m ?== x
     }
   )
 
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 22aa33f785..4dc3f12b7e 100644
--- a/kernel-laws/src/test/scala/cats/kernel/laws/LawTests.scala
+++ b/kernel-laws/src/test/scala/cats/kernel/laws/LawTests.scala
@@ -77,6 +77,14 @@ class LawTests extends FunSuite with Discipline {
   //laws[GroupLaws, Double].check(_.commutativeGroup) // approximately associative
   laws[GroupLaws, BigInt].check(_.commutativeGroup)
 
+  {
+    // default Arbitrary[BigDecimal] is a bit too intense :/
+    implicit val arbBigDecimal: Arbitrary[BigDecimal] =
+      Arbitrary(arbitrary[Double].map(n => BigDecimal(n.toString)))
+    laws[OrderLaws, BigDecimal].check(_.order)
+    laws[GroupLaws, BigDecimal].check(_.commutativeGroup)
+  }
+
   laws[GroupLaws, (Int, Int)].check(_.band)
 
   laws[GroupLaws, Unit].check(_.boundedSemilattice)
diff --git a/kernel/src/main/scala/cats/kernel/instances/all.scala b/kernel/src/main/scala/cats/kernel/instances/all.scala
index 3fc5b82b5a..b519278ef1 100644
--- a/kernel/src/main/scala/cats/kernel/instances/all.scala
+++ b/kernel/src/main/scala/cats/kernel/instances/all.scala
@@ -4,7 +4,8 @@ package instances
 package object all extends AllInstances
 
 trait AllInstances
-    extends BigIntInstances
+    extends BigDecimalInstances
+    with BigIntInstances
     with BooleanInstances
     with ByteInstances
     with CharInstances
diff --git a/kernel/src/main/scala/cats/kernel/instances/bigDecimal.scala b/kernel/src/main/scala/cats/kernel/instances/bigDecimal.scala
new file mode 100644
index 0000000000..28203cb91e
--- /dev/null
+++ b/kernel/src/main/scala/cats/kernel/instances/bigDecimal.scala
@@ -0,0 +1,33 @@
+package cats.kernel
+package instances
+
+package object bigDecimal extends BigDecimalInstances // scalastyle:ignore package.object.name
+
+trait BigDecimalInstances {
+  implicit val catsKernelStdOrderForBigDecimal: Order[BigDecimal] =
+    new BigDecimalOrder
+  implicit val catsKernelStdGroupForBigDecimal: CommutativeGroup[BigDecimal] =
+    new BigDecimalGroup
+}
+
+class BigDecimalGroup extends CommutativeGroup[BigDecimal] {
+  val empty: BigDecimal = BigDecimal(0)
+  def combine(x: BigDecimal, y: BigDecimal): BigDecimal = x + y
+  def inverse(x: BigDecimal): BigDecimal = -x
+  override def remove(x: BigDecimal, y: BigDecimal): BigDecimal = x - y
+}
+
+class BigDecimalOrder extends Order[BigDecimal] {
+
+  def compare(x: BigDecimal, y: BigDecimal): Int = x compare y
+
+  override def eqv(x: BigDecimal, y: BigDecimal): Boolean = x == y
+  override def neqv(x: BigDecimal, y: BigDecimal): Boolean = x != y
+  override def gt(x: BigDecimal, y: BigDecimal): Boolean = x > y
+  override def gteqv(x: BigDecimal, y: BigDecimal): Boolean = x >= y
+  override def lt(x: BigDecimal, y: BigDecimal): Boolean = x < y
+  override def lteqv(x: BigDecimal, y: BigDecimal): Boolean = x <= y
+
+  override def min(x: BigDecimal, y: BigDecimal): BigDecimal = x min y
+  override def max(x: BigDecimal, y: BigDecimal): BigDecimal = x max y
+}