diff --git a/core/src/main/scala/cats/evidence/Is.scala b/core/src/main/scala/cats/evidence/Is.scala
index d9b2a9c1f1..632f96a3e2 100644
--- a/core/src/main/scala/cats/evidence/Is.scala
+++ b/core/src/main/scala/cats/evidence/Is.scala
@@ -1,6 +1,7 @@
 package cats.evidence
 
 import cats.Id
+import cats.arrow._
 
 /**
  * A value of `A Is B` is proof that the types `A` and `B` are the same. More
@@ -65,7 +66,19 @@ abstract class Is[A, B] extends Serializable {
     substitute[A =:= ?](implicitly[A =:= A])
 }
 
-object Is {
+sealed abstract class IsInstances {
+  import Is._
+
+  /**
+   * The category instance on Leibniz categories.
+   */
+  implicit val leibniz: Category[Is] = new Category[Is] {
+    def id[A]: A Is A = refl[A]
+    def compose[A, B, C](bc: B Is C, ab: A Is B): A Is C = bc.compose(ab)
+  }
+}
+
+object Is extends IsInstances {
 
   /**
    * In truth, "all values of `A Is B` are `refl`". `reflAny` is that
diff --git a/tests/src/test/scala/cats/tests/IsSuite.scala b/tests/src/test/scala/cats/tests/IsSuite.scala
index 6d2ef5050a..26f5bb827e 100644
--- a/tests/src/test/scala/cats/tests/IsSuite.scala
+++ b/tests/src/test/scala/cats/tests/IsSuite.scala
@@ -1,9 +1,25 @@
 package cats
 package tests
 
+import cats.arrow._
+import cats.kernel.laws.discipline.SerializableTests
+import cats.laws.discipline.CategoryTests
+import org.scalacheck.{Arbitrary, Gen}
+
 class IsSuite extends CatsSuite {
   import evidence._
 
+  implicit def arbIs[A, B](implicit ev: A Is B): Arbitrary[A Is B] = Arbitrary(Gen.const(ev))
+  implicit def eqIs[A, B]: Eq[A Is B] = Eq.fromUniversalEquals
+
+  trait Top {
+    def foo: String = this.getClass.getName
+  }
+  case class Bottom() extends Top
+
+  checkAll("Is[Bottom, Bottom]", CategoryTests[Is].category[Bottom, Bottom, Bottom, Bottom])
+  checkAll("Category[Is]", SerializableTests.serializable(Category[Is]))
+
   test("syntax") {
     trait Bar