diff --git a/core/src/main/scala/cats/FunctorEmpty.scala b/core/src/main/scala/cats/FunctorFilter.scala
similarity index 76%
rename from core/src/main/scala/cats/FunctorEmpty.scala
rename to core/src/main/scala/cats/FunctorFilter.scala
index 21c75a119e0..90a43c0e640 100644
--- a/core/src/main/scala/cats/FunctorEmpty.scala
+++ b/core/src/main/scala/cats/FunctorFilter.scala
@@ -3,10 +3,10 @@ package cats
 import simulacrum.typeclass
 
 /**
- * `FunctorEmpty[F]` allows you to `map` and filter out elements simultaneously.
+ * `FunctorFilter[F]` allows you to `map` and filter out elements simultaneously.
  */
 @typeclass
-trait FunctorEmpty[F[_]] extends Serializable {
+trait FunctorFilter[F[_]] extends Serializable {
   def functor: Functor[F]
 
   def mapFilter[A, B](fa: F[A])(f: A => Option[B]): F[B]
diff --git a/core/src/main/scala/cats/TraverseEmpty.scala b/core/src/main/scala/cats/TraverseFilter.scala
similarity index 84%
rename from core/src/main/scala/cats/TraverseEmpty.scala
rename to core/src/main/scala/cats/TraverseFilter.scala
index 5dc3bd631fa..ad15ee7311d 100644
--- a/core/src/main/scala/cats/TraverseEmpty.scala
+++ b/core/src/main/scala/cats/TraverseFilter.scala
@@ -3,7 +3,7 @@ package cats
 import simulacrum.typeclass
 
 /**
- * `TraverseEmpty`, also known as `Witherable`, represents list-like structures
+ * `TraverseFilter`, also known as `Witherable`, represents list-like structures
  * that can essentially have a `traverse` and a `filter` applied as a single
  * combined operation (`traverseFilter`).
  *
@@ -11,7 +11,7 @@ import simulacrum.typeclass
  */
 
 @typeclass
-trait TraverseEmpty[F[_]] extends FunctorEmpty[F] {
+trait TraverseFilter[F[_]] extends FunctorFilter[F] {
   def traverse: Traverse[F]
 
   final override def functor: Functor[F] = traverse
diff --git a/core/src/main/scala/cats/data/Chain.scala b/core/src/main/scala/cats/data/Chain.scala
index 96575bcf8a7..e577de3e53c 100644
--- a/core/src/main/scala/cats/data/Chain.scala
+++ b/core/src/main/scala/cats/data/Chain.scala
@@ -617,7 +617,7 @@ private[data] sealed abstract class ChainInstances extends ChainInstances1 {
       }
     }
 
-  implicit val catsDataTraverseEmptyForChain: TraverseEmpty[Chain] = new TraverseEmpty[Chain] {
+  implicit val catsDataTraverseFilterForChain: TraverseFilter[Chain] = new TraverseFilter[Chain] {
     def traverse: Traverse[Chain] = Chain.catsDataInstancesForChain
 
     override def filter[A](fa: Chain[A])(f: A => Boolean): Chain[A] = fa.filter(f)
diff --git a/core/src/main/scala/cats/data/Const.scala b/core/src/main/scala/cats/data/Const.scala
index e8beb676d8b..9532cc74406 100644
--- a/core/src/main/scala/cats/data/Const.scala
+++ b/core/src/main/scala/cats/data/Const.scala
@@ -87,7 +87,7 @@ private[data] sealed abstract class ConstInstances extends ConstInstances0 {
       fa.traverse(f)
   }
 
-  implicit def catsDataTraverseEmptyForConst[C]: TraverseEmpty[Const[C, ?]] = new TraverseEmpty[Const[C, ?]] {
+  implicit def catsDataTraverseFilterForConst[C]: TraverseFilter[Const[C, ?]] = new TraverseFilter[Const[C, ?]] {
 
     override def mapFilter[A, B](fa: Const[C, A])(f: (A) => Option[B]): Const[C, B] = fa.retag
 
diff --git a/core/src/main/scala/cats/data/EitherT.scala b/core/src/main/scala/cats/data/EitherT.scala
index a35201c2b65..583ad070890 100644
--- a/core/src/main/scala/cats/data/EitherT.scala
+++ b/core/src/main/scala/cats/data/EitherT.scala
@@ -507,9 +507,9 @@ private[data] abstract class EitherTInstances extends EitherTInstances1 {
         EitherT(F.defer(fa.value))
     }
 
-  implicit def catsDataTraverseEmptyForEitherT[F[_], L](implicit F0: TraverseEmpty[F]): TraverseEmpty[EitherT[F, L, ?]] =
-    new EitherTFunctorEmpty[F, L] with TraverseEmpty[EitherT[F, L, ?]] {
-      implicit def F: FunctorEmpty[F] = F0
+  implicit def catsDataTraverseFilterForEitherT[F[_], L](implicit F0: TraverseFilter[F]): TraverseFilter[EitherT[F, L, ?]] =
+    new EitherTFunctorFilter[F, L] with TraverseFilter[EitherT[F, L, ?]] {
+      implicit def F: FunctorFilter[F] = F0
       def traverse: Traverse[EitherT[F, L, ?]] = catsDataTraverseForEitherT[F, L](F0.traverse)
 
       def traverseFilter[G[_], A, B]
@@ -560,8 +560,8 @@ private[data] abstract class EitherTInstances1 extends EitherTInstances2 {
         fa.ensureOr(error)(predicate)(F)
     }
 
-  implicit def catsDataFunctorEmptyForEitherT[F[_], L](implicit F0: FunctorEmpty[F]): FunctorEmpty[EitherT[F, L, ?]] =
-    new EitherTFunctorEmpty[F, L] { implicit def F = F0 }
+  implicit def catsDataFunctorFilterForEitherT[F[_], L](implicit F0: FunctorFilter[F]): FunctorFilter[EitherT[F, L, ?]] =
+    new EitherTFunctorFilter[F, L] { implicit def F = F0 }
 }
 
 private[data] abstract class EitherTInstances2 extends EitherTInstances3 {
@@ -722,8 +722,8 @@ private[data] sealed trait EitherTOrder[F[_], L, A] extends Order[EitherT[F, L,
   override def compare(x: EitherT[F, L, A], y: EitherT[F, L, A]): Int = x compare y
 }
 
-private[data] sealed trait EitherTFunctorEmpty[F[_], E] extends FunctorEmpty[EitherT[F, E, ?]] {
-  implicit def F: FunctorEmpty[F]
+private[data] sealed trait EitherTFunctorFilter[F[_], E] extends FunctorFilter[EitherT[F, E, ?]] {
+  implicit def F: FunctorFilter[F]
 
   override def functor: Functor[EitherT[F, E, ?]] = EitherT.catsDataFunctorForEitherT[F, E](F.functor)
 
diff --git a/core/src/main/scala/cats/data/Nested.scala b/core/src/main/scala/cats/data/Nested.scala
index efc8f520eca..871c7e90fd0 100644
--- a/core/src/main/scala/cats/data/Nested.scala
+++ b/core/src/main/scala/cats/data/Nested.scala
@@ -54,10 +54,10 @@ private[data] sealed abstract class NestedInstances extends NestedInstances0 {
         Nested(F.defer(fa.value))
     }
 
-  implicit def catsDataTraverseEmptyForNested[F[_], G[_]](implicit F0: Traverse[F], G0: TraverseEmpty[G]): TraverseEmpty[Nested[F, G, ?]] =
-    new NestedTraverseEmpty[F, G] {
+  implicit def catsDataTraverseFilterForNested[F[_], G[_]](implicit F0: Traverse[F], G0: TraverseFilter[G]): TraverseFilter[Nested[F, G, ?]] =
+    new NestedTraverseFilter[F, G] {
       implicit val F: Traverse[F] = F0
-      implicit val G: TraverseEmpty[G] = G0
+      implicit val G: TraverseFilter[G] = G0
     }
 
 
@@ -323,10 +323,10 @@ private[data] trait NestedInvariantSemigroupalApply[F[_], G[_]] extends Invarian
     Nested(FG.product(fa.value, fb.value))
 }
 
-private[data] abstract class NestedTraverseEmpty[F[_], G[_]] extends TraverseEmpty[Nested[F, G, ?]] {
+private[data] abstract class NestedTraverseFilter[F[_], G[_]] extends TraverseFilter[Nested[F, G, ?]] {
   implicit val F: Traverse[F]
 
-  implicit val G: TraverseEmpty[G]
+  implicit val G: TraverseFilter[G]
 
   def traverse: Traverse[Nested[F, G, ?]] = Nested.catsDataTraverseForNested(F, G.traverse)
 
diff --git a/core/src/main/scala/cats/data/OptionT.scala b/core/src/main/scala/cats/data/OptionT.scala
index 9552ee855d2..9e057eec660 100644
--- a/core/src/main/scala/cats/data/OptionT.scala
+++ b/core/src/main/scala/cats/data/OptionT.scala
@@ -235,8 +235,8 @@ private[data] sealed abstract class OptionTInstances extends OptionTInstances0 {
         OptionT(F.defer(fa.value))
     }
 
-  implicit def optionTFunctorEmpty[F[_]: Functor]: FunctorEmpty[OptionT[F, ?]] = {
-    new FunctorEmpty[OptionT[F, ?]] {
+  implicit def optionTFunctorFilter[F[_]: Functor]: FunctorFilter[OptionT[F, ?]] = {
+    new FunctorFilter[OptionT[F, ?]] {
       override val functor: Functor[OptionT[F, ?]] = OptionT.catsDataFunctorForOptionT[F]
 
       override def mapFilter[A, B](fa: OptionT[F, A])(f: (A) => Option[B]): OptionT[F, B] = fa.subflatMap(f)
diff --git a/core/src/main/scala/cats/instances/list.scala b/core/src/main/scala/cats/instances/list.scala
index 90761bfa274..7ef2972a0b7 100644
--- a/core/src/main/scala/cats/instances/list.scala
+++ b/core/src/main/scala/cats/instances/list.scala
@@ -145,7 +145,7 @@ trait ListInstances extends cats.kernel.instances.ListInstances {
 }
 
 trait ListInstancesBinCompat0 {
-  implicit val catsStdTraverseEmptyForList: TraverseEmpty[List] = new TraverseEmpty[List] {
+  implicit val catsStdTraverseFilterForList: TraverseFilter[List] = new TraverseFilter[List] {
     val traverse: Traverse[List] = cats.instances.list.catsStdInstancesForList
 
     override def mapFilter[A, B](fa: List[A])(f: (A) => Option[B]): List[B] = fa.collect(Function.unlift(f))
diff --git a/core/src/main/scala/cats/instances/map.scala b/core/src/main/scala/cats/instances/map.scala
index 745caa60e43..fda0d300523 100644
--- a/core/src/main/scala/cats/instances/map.scala
+++ b/core/src/main/scala/cats/instances/map.scala
@@ -109,8 +109,8 @@ trait MapInstancesBinCompat0 {
     }
   }
 
-  implicit def catsStdFunctorEmptyForMap[K]: FunctorEmpty[Map[K, ?]] = {
-    new FunctorEmpty[Map[K, ?]] {
+  implicit def catsStdFunctorFilterForMap[K]: FunctorFilter[Map[K, ?]] = {
+    new FunctorFilter[Map[K, ?]] {
 
       val functor: Functor[Map[K, ?]] = cats.instances.map.catsStdInstancesForMap[K]
 
diff --git a/core/src/main/scala/cats/instances/option.scala b/core/src/main/scala/cats/instances/option.scala
index a03e004b643..16d72006b0a 100644
--- a/core/src/main/scala/cats/instances/option.scala
+++ b/core/src/main/scala/cats/instances/option.scala
@@ -123,7 +123,7 @@ trait OptionInstances extends cats.kernel.instances.OptionInstances {
 }
 
 trait OptionInstancesBinCompat0 {
-  implicit val catsStdTraverseEmptyForOption: TraverseEmpty[Option] = new TraverseEmpty[Option] {
+  implicit val catsStdTraverseFilterForOption: TraverseFilter[Option] = new TraverseFilter[Option] {
     val traverse: Traverse[Option] = cats.instances.option.catsStdInstancesForOption
 
     override def mapFilter[A, B](fa: Option[A])(f: (A) => Option[B]): Option[B] = fa.flatMap(f)
diff --git a/core/src/main/scala/cats/instances/sortedMap.scala b/core/src/main/scala/cats/instances/sortedMap.scala
index 708841d1491..a23a18f1502 100644
--- a/core/src/main/scala/cats/instances/sortedMap.scala
+++ b/core/src/main/scala/cats/instances/sortedMap.scala
@@ -1,6 +1,6 @@
 package cats.instances
 
-import cats.{Always, Applicative, Eval, FlatMap, Foldable, Monoid, Order, Show, Traverse, TraverseEmpty}
+import cats.{Always, Applicative, Eval, FlatMap, Foldable, Monoid, Order, Show, Traverse, TraverseFilter}
 import cats.kernel._
 import cats.kernel.instances.StaticMethods
 
@@ -168,8 +168,8 @@ class SortedMapMonoid[K, V](implicit V: Semigroup[V], O: Order[K]) extends Monoi
 }
 
 trait SortedMapInstancesBinCompat0 {
-  implicit def catsStdTraverseEmptyForSortedMap[K: Order]: TraverseEmpty[SortedMap[K, ?]] =
-    new TraverseEmpty[SortedMap[K, ?]] {
+  implicit def catsStdTraverseFilterForSortedMap[K: Order]: TraverseFilter[SortedMap[K, ?]] =
+    new TraverseFilter[SortedMap[K, ?]] {
 
       implicit val ordering: Ordering[K] = Order[K].toOrdering
 
diff --git a/core/src/main/scala/cats/instances/stream.scala b/core/src/main/scala/cats/instances/stream.scala
index c33730c315e..1d97c90fb03 100644
--- a/core/src/main/scala/cats/instances/stream.scala
+++ b/core/src/main/scala/cats/instances/stream.scala
@@ -155,7 +155,7 @@ trait StreamInstances extends cats.kernel.instances.StreamInstances {
 }
 
 trait StreamInstancesBinCompat0 {
-  implicit val catsStdTraverseEmptyForStream: TraverseEmpty[Stream] = new TraverseEmpty[Stream] {
+  implicit val catsStdTraverseFilterForStream: TraverseFilter[Stream] = new TraverseFilter[Stream] {
     val traverse: Traverse[Stream] = cats.instances.stream.catsStdInstancesForStream
 
     override def mapFilter[A, B](fa: Stream[A])(f: (A) => Option[B]): Stream[B] = {
diff --git a/core/src/main/scala/cats/instances/vector.scala b/core/src/main/scala/cats/instances/vector.scala
index e2bafc1237a..1b1ddec7409 100644
--- a/core/src/main/scala/cats/instances/vector.scala
+++ b/core/src/main/scala/cats/instances/vector.scala
@@ -116,7 +116,7 @@ trait VectorInstances extends cats.kernel.instances.VectorInstances {
 }
 
 trait VectorInstancesBinCompat0 {
-  implicit val catsStdTraverseEmptyForVector: TraverseEmpty[Vector] = new TraverseEmpty[Vector] {
+  implicit val catsStdTraverseFilterForVector: TraverseFilter[Vector] = new TraverseFilter[Vector] {
     val traverse: Traverse[Vector] = cats.instances.vector.catsStdInstancesForVector
 
     override def mapFilter[A, B](fa: Vector[A])(f: (A) => Option[B]): Vector[B] =
diff --git a/core/src/main/scala/cats/syntax/all.scala b/core/src/main/scala/cats/syntax/all.scala
index 92d7f2b59d8..d131c8bd259 100644
--- a/core/src/main/scala/cats/syntax/all.scala
+++ b/core/src/main/scala/cats/syntax/all.scala
@@ -72,5 +72,5 @@ trait AllSyntaxBinCompat1
 
 trait AllSyntaxBinCompat2
   extends ParallelTraverseSyntax
-    with TraverseEmptySyntax
-    with FunctorEmptySyntax
+    with TraverseFilterSyntax
+    with FunctorFilterSyntax
diff --git a/core/src/main/scala/cats/syntax/functorEmpty.scala b/core/src/main/scala/cats/syntax/functorEmpty.scala
deleted file mode 100644
index ee687de18ff..00000000000
--- a/core/src/main/scala/cats/syntax/functorEmpty.scala
+++ /dev/null
@@ -1,4 +0,0 @@
-package cats
-package syntax
-
-trait FunctorEmptySyntax extends FunctorEmpty.ToFunctorEmptyOps
diff --git a/core/src/main/scala/cats/syntax/functorFilter.scala b/core/src/main/scala/cats/syntax/functorFilter.scala
new file mode 100644
index 00000000000..a80b6c2618e
--- /dev/null
+++ b/core/src/main/scala/cats/syntax/functorFilter.scala
@@ -0,0 +1,4 @@
+package cats
+package syntax
+
+trait FunctorFilterSyntax extends FunctorFilter.ToFunctorFilterOps
diff --git a/core/src/main/scala/cats/syntax/package.scala b/core/src/main/scala/cats/syntax/package.scala
index dd6a5fbf562..c336eecd139 100644
--- a/core/src/main/scala/cats/syntax/package.scala
+++ b/core/src/main/scala/cats/syntax/package.scala
@@ -28,7 +28,7 @@ package object syntax {
   object flatMap extends FlatMapSyntax
   object foldable extends FoldableSyntax
   object functor extends FunctorSyntax
-  object functorEmpty extends FunctorEmptySyntax
+  object functorFilter extends FunctorFilterSyntax
   object group extends GroupSyntax
   object invariant extends InvariantSyntax
   object ior extends IorSyntax
@@ -50,7 +50,7 @@ package object syntax {
   object show extends ShowSyntax
   object strong extends StrongSyntax
   object traverse extends TraverseSyntax
-  object traverseEmpty extends TraverseEmptySyntax
+  object traverseFilter extends TraverseFilterSyntax
   object nonEmptyTraverse extends NonEmptyTraverseSyntax
   object unorderedTraverse extends UnorderedTraverseSyntax
   object validated extends ValidatedSyntax with ValidatedExtensionSyntax
diff --git a/core/src/main/scala/cats/syntax/traverseEmpty.scala b/core/src/main/scala/cats/syntax/traverseEmpty.scala
deleted file mode 100644
index bfe49e712f2..00000000000
--- a/core/src/main/scala/cats/syntax/traverseEmpty.scala
+++ /dev/null
@@ -1,4 +0,0 @@
-package cats
-package syntax
-
-trait TraverseEmptySyntax extends TraverseEmpty.ToTraverseEmptyOps
diff --git a/core/src/main/scala/cats/syntax/traverseFilter.scala b/core/src/main/scala/cats/syntax/traverseFilter.scala
new file mode 100644
index 00000000000..794caeddee1
--- /dev/null
+++ b/core/src/main/scala/cats/syntax/traverseFilter.scala
@@ -0,0 +1,4 @@
+package cats
+package syntax
+
+trait TraverseFilterSyntax extends TraverseFilter.ToTraverseFilterOps
diff --git a/laws/src/main/scala/cats/laws/FunctorEmptyLaws.scala b/laws/src/main/scala/cats/laws/FunctorFilterLaws.scala
similarity index 80%
rename from laws/src/main/scala/cats/laws/FunctorEmptyLaws.scala
rename to laws/src/main/scala/cats/laws/FunctorFilterLaws.scala
index 814580896c5..32af361b1d7 100644
--- a/laws/src/main/scala/cats/laws/FunctorEmptyLaws.scala
+++ b/laws/src/main/scala/cats/laws/FunctorFilterLaws.scala
@@ -2,8 +2,8 @@ package cats
 package laws
 
 
-trait FunctorEmptyLaws[F[_]] {
-  implicit def F: FunctorEmpty[F]
+trait FunctorFilterLaws[F[_]] {
+  implicit def F: FunctorFilter[F]
 
 
   implicit def functor: Functor[F] = F.functor
@@ -32,7 +32,7 @@ trait FunctorEmptyLaws[F[_]] {
   }
 }
 
-object FunctorEmptyLaws {
-  def apply[F[_]](implicit ev: FunctorEmpty[F]): FunctorEmptyLaws[F] =
-    new FunctorEmptyLaws[F] { def F: FunctorEmpty[F] = ev }
+object FunctorFilterLaws {
+  def apply[F[_]](implicit ev: FunctorFilter[F]): FunctorFilterLaws[F] =
+    new FunctorFilterLaws[F] { def F: FunctorFilter[F] = ev }
 }
diff --git a/laws/src/main/scala/cats/laws/TraverseEmptyLaws.scala b/laws/src/main/scala/cats/laws/TraverseFilterLaws.scala
similarity index 83%
rename from laws/src/main/scala/cats/laws/TraverseEmptyLaws.scala
rename to laws/src/main/scala/cats/laws/TraverseFilterLaws.scala
index 5c98a459cbb..bd799fa8f67 100644
--- a/laws/src/main/scala/cats/laws/TraverseEmptyLaws.scala
+++ b/laws/src/main/scala/cats/laws/TraverseFilterLaws.scala
@@ -5,8 +5,8 @@ import cats.data.Nested
 import cats.syntax.all._
 import cats.instances.option._
 
-trait TraverseEmptyLaws[F[_]] extends FunctorEmptyLaws[F] {
-  implicit override def F: TraverseEmpty[F]
+trait TraverseFilterLaws[F[_]] extends FunctorFilterLaws[F] {
+  implicit override def F: TraverseFilter[F]
 
   def traverseFilterIdentity[G[_]: Applicative, A](fa: F[A]): IsEq[G[F[A]]] = {
     fa.traverseFilter(_.some.pure[G]) <-> fa.pure[G]
@@ -35,7 +35,7 @@ trait TraverseEmptyLaws[F[_]] extends FunctorEmptyLaws[F] {
   }
 }
 
-object TraverseEmptyLaws {
-  def apply[F[_]](implicit ev: TraverseEmpty[F]): TraverseEmptyLaws[F] =
-    new TraverseEmptyLaws[F] { def F: TraverseEmpty[F] = ev }
+object TraverseFilterLaws {
+  def apply[F[_]](implicit ev: TraverseFilter[F]): TraverseFilterLaws[F] =
+    new TraverseFilterLaws[F] { def F: TraverseFilter[F] = ev }
 }
diff --git a/laws/src/main/scala/cats/laws/discipline/FunctorEmptyTests.scala b/laws/src/main/scala/cats/laws/discipline/FunctorFilterTests.scala
similarity index 79%
rename from laws/src/main/scala/cats/laws/discipline/FunctorEmptyTests.scala
rename to laws/src/main/scala/cats/laws/discipline/FunctorFilterTests.scala
index 38fe5e7a670..01fead48a2d 100644
--- a/laws/src/main/scala/cats/laws/discipline/FunctorEmptyTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/FunctorFilterTests.scala
@@ -6,10 +6,10 @@ import org.scalacheck.Prop.forAll
 import org.scalacheck.Arbitrary
 import org.typelevel.discipline.Laws
 
-trait FunctorEmptyTests[F[_]] extends Laws {
-  def laws: FunctorEmptyLaws[F]
+trait FunctorFilterTests[F[_]] extends Laws {
+  def laws: FunctorFilterLaws[F]
 
-  def functorEmpty[A, B, C](implicit
+  def functorFilter[A, B, C](implicit
                             ArbFA: Arbitrary[F[A]],
                             ArbFABoo: Arbitrary[PartialFunction[A, B]],
                             ArbFOA: Arbitrary[F[Option[A]]],
@@ -22,7 +22,7 @@ trait FunctorEmptyTests[F[_]] extends Laws {
                             EqFC: Eq[F[C]]
                            ): RuleSet = {
     new DefaultRuleSet(
-      name = "functorEmpty",
+      name = "functorFilter",
       parent = None,
       "mapFilter composition" -> forAll(laws.mapFilterComposition[A, B, C] _),
       "mapFilter map consistency" -> forAll(laws.mapFilterMapConsistency[A, B] _),
@@ -33,7 +33,7 @@ trait FunctorEmptyTests[F[_]] extends Laws {
   }
 }
 
-object FunctorEmptyTests {
-  def apply[F[_]: FunctorEmpty]: FunctorEmptyTests[F] =
-    new FunctorEmptyTests[F] { def laws: FunctorEmptyLaws[F] = FunctorEmptyLaws[F] }
+object FunctorFilterTests {
+  def apply[F[_]: FunctorFilter]: FunctorFilterTests[F] =
+    new FunctorFilterTests[F] { def laws: FunctorFilterLaws[F] = FunctorFilterLaws[F] }
 }
diff --git a/laws/src/main/scala/cats/laws/discipline/TraverseEmptyTests.scala b/laws/src/main/scala/cats/laws/discipline/TraverseFilterTests.scala
similarity index 80%
rename from laws/src/main/scala/cats/laws/discipline/TraverseEmptyTests.scala
rename to laws/src/main/scala/cats/laws/discipline/TraverseFilterTests.scala
index d163b444edb..77dc281eec3 100644
--- a/laws/src/main/scala/cats/laws/discipline/TraverseEmptyTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/TraverseFilterTests.scala
@@ -7,10 +7,10 @@ import org.scalacheck.Prop.forAll
 import org.scalacheck.Arbitrary
 import cats.instances.option._
 
-trait TraverseEmptyTests[F[_]] extends FunctorEmptyTests[F] {
-  def laws: TraverseEmptyLaws[F]
+trait TraverseFilterTests[F[_]] extends FunctorFilterTests[F] {
+  def laws: TraverseFilterLaws[F]
 
-  def traverseEmpty[A, B, C](implicit
+  def traverseFilter[A, B, C](implicit
                              ArbFA: Arbitrary[F[A]],
                              ArbFOA: Arbitrary[F[Option[A]]],
                              ArbFABoo: Arbitrary[PartialFunction[A, B]],
@@ -29,8 +29,8 @@ trait TraverseEmptyTests[F[_]] extends FunctorEmptyTests[F] {
                              EqMNFC: Eq[Nested[Option, Option, F[C]]]
                             ): RuleSet = {
     new DefaultRuleSet(
-      name = "traverseEmpty",
-      parent = Some(functorEmpty[A, B, C]),
+      name = "traverseFilter",
+      parent = Some(functorFilter[A, B, C]),
       "traverseFilter identity" -> forAll(laws.traverseFilterIdentity[Option, A] _),
       "traverseFilter nested composition" -> forAll(laws.traverseFilterComposition[A, B, C, Option, Option] _),
       "traverseFilter consistent with traverse" -> forAll(laws.traverseFilterConsistentWithTraverse[Option, A] _),
@@ -39,7 +39,7 @@ trait TraverseEmptyTests[F[_]] extends FunctorEmptyTests[F] {
   }
 }
 
-object TraverseEmptyTests {
-  def apply[F[_]: TraverseEmpty]: TraverseEmptyTests[F] =
-    new TraverseEmptyTests[F] { def laws: TraverseEmptyLaws[F] = TraverseEmptyLaws[F] }
+object TraverseFilterTests {
+  def apply[F[_]: TraverseFilter]: TraverseFilterTests[F] =
+    new TraverseFilterTests[F] { def laws: TraverseFilterLaws[F] = TraverseFilterLaws[F] }
 }
diff --git a/tests/src/test/scala/cats/tests/ChainSuite.scala b/tests/src/test/scala/cats/tests/ChainSuite.scala
index 65608886d03..54fed688738 100644
--- a/tests/src/test/scala/cats/tests/ChainSuite.scala
+++ b/tests/src/test/scala/cats/tests/ChainSuite.scala
@@ -2,7 +2,7 @@ package cats
 package tests
 
 import cats.data.Chain
-import cats.laws.discipline.{AlternativeTests, CoflatMapTests, MonadTests, SerializableTests, TraverseEmptyTests, TraverseTests}
+import cats.laws.discipline.{AlternativeTests, CoflatMapTests, MonadTests, SerializableTests, TraverseFilterTests, TraverseTests}
 import cats.kernel.laws.discipline.{EqTests, MonoidTests, OrderTests, PartialOrderTests}
 import cats.laws.discipline.arbitrary._
 
@@ -26,8 +26,8 @@ class ChainSuite extends CatsSuite {
   checkAll("Order[Chain]", SerializableTests.serializable(Order[Chain[Int]]))
 
 
-  checkAll("Chain[Int]", TraverseEmptyTests[Chain].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[Chain]", SerializableTests.serializable(TraverseEmpty[Chain]))
+  checkAll("Chain[Int]", TraverseFilterTests[Chain].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[Chain]", SerializableTests.serializable(TraverseFilter[Chain]))
 
   {
     implicit val partialOrder = ListWrapper.partialOrder[Int]
diff --git a/tests/src/test/scala/cats/tests/ConstSuite.scala b/tests/src/test/scala/cats/tests/ConstSuite.scala
index e1f7756da75..d233f91ac50 100644
--- a/tests/src/test/scala/cats/tests/ConstSuite.scala
+++ b/tests/src/test/scala/cats/tests/ConstSuite.scala
@@ -21,8 +21,8 @@ class ConstSuite extends CatsSuite {
   checkAll("Const[String, Int] with Option", TraverseTests[Const[String, ?]].traverse[Int, Int, Int, Int, Option, Option])
   checkAll("Traverse[Const[String, ?]]", SerializableTests.serializable(Traverse[Const[String, ?]]))
 
-  checkAll("Const[String, Int]", TraverseEmptyTests[Const[String, ?]].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[Const[String, ?]]", SerializableTests.serializable(TraverseEmpty[Const[String, ?]]))
+  checkAll("Const[String, Int]", TraverseFilterTests[Const[String, ?]].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[Const[String, ?]]", SerializableTests.serializable(TraverseFilter[Const[String, ?]]))
 
   // Get Apply[Const[C : Semigroup, ?]], not Applicative[Const[C : Monoid, ?]]
   {
diff --git a/tests/src/test/scala/cats/tests/EitherTSuite.scala b/tests/src/test/scala/cats/tests/EitherTSuite.scala
index 296453228cd..7f32f456663 100644
--- a/tests/src/test/scala/cats/tests/EitherTSuite.scala
+++ b/tests/src/test/scala/cats/tests/EitherTSuite.scala
@@ -48,24 +48,24 @@ class EitherTSuite extends CatsSuite {
   }
 
   {
-    //If a TraverseEmpty for F is defined
-    implicit val F = ListWrapper.traverseEmpty
+    //If a TraverseFilter for F is defined
+    implicit val F = ListWrapper.traverseFilter
 
     checkAll("EitherT[ListWrapper, Int, ?]",
-      TraverseEmptyTests[EitherT[ListWrapper, Int, ?]].traverseEmpty[Int, Int, Int])
-    checkAll("TraverseEmpty[EitherT[ListWrapper, Int, ?]]",
-      SerializableTests.serializable(TraverseEmpty[EitherT[ListWrapper, Int, ?]]))
+      TraverseFilterTests[EitherT[ListWrapper, Int, ?]].traverseFilter[Int, Int, Int])
+    checkAll("TraverseFilter[EitherT[ListWrapper, Int, ?]]",
+      SerializableTests.serializable(TraverseFilter[EitherT[ListWrapper, Int, ?]]))
 
   }
 
   {
-    //If a FunctorEmpty for F is defined
-    implicit val F = ListWrapper.functorEmpty
+    //If a functorFilter for F is defined
+    implicit val F = ListWrapper.functorFilter
 
     checkAll("EitherT[ListWrapper, Int, ?]",
-      FunctorEmptyTests[EitherT[ListWrapper, Int, ?]].functorEmpty[Int, Int, Int])
-    checkAll("FunctorEmpty[EitherT[ListWrapper, Int, ?]]",
-      SerializableTests.serializable(FunctorEmpty[EitherT[ListWrapper, Int, ?]]))
+      FunctorFilterTests[EitherT[ListWrapper, Int, ?]].functorFilter[Int, Int, Int])
+    checkAll("FunctorFilter[EitherT[ListWrapper, Int, ?]]",
+      SerializableTests.serializable(FunctorFilter[EitherT[ListWrapper, Int, ?]]))
 
   }
 
diff --git a/tests/src/test/scala/cats/tests/ListSuite.scala b/tests/src/test/scala/cats/tests/ListSuite.scala
index a74cbcc77a9..1e8ed70e04e 100644
--- a/tests/src/test/scala/cats/tests/ListSuite.scala
+++ b/tests/src/test/scala/cats/tests/ListSuite.scala
@@ -2,7 +2,7 @@ package cats
 package tests
 
 import cats.data.{NonEmptyList, ZipList}
-import cats.laws.discipline.{AlternativeTests, CoflatMapTests, CommutativeApplyTests, MonadTests, SemigroupalTests, SerializableTests, TraverseEmptyTests, TraverseTests}
+import cats.laws.discipline.{AlternativeTests, CoflatMapTests, CommutativeApplyTests, MonadTests, SemigroupalTests, SerializableTests, TraverseFilterTests, TraverseTests}
 import cats.laws.discipline.arbitrary._
 
 class ListSuite extends CatsSuite {
@@ -22,8 +22,8 @@ class ListSuite extends CatsSuite {
   checkAll("List[Int]", MonadTests[List].monad[Int, Int, Int])
   checkAll("Monad[List]", SerializableTests.serializable(Monad[List]))
 
-  checkAll("List[Int]", TraverseEmptyTests[List].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[List]", SerializableTests.serializable(TraverseEmpty[List]))
+  checkAll("List[Int]", TraverseFilterTests[List].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[List]", SerializableTests.serializable(TraverseFilter[List]))
 
 
   checkAll("ZipList[Int]", CommutativeApplyTests[ZipList].commutativeApply[Int, Int, Int])
diff --git a/tests/src/test/scala/cats/tests/ListWrapper.scala b/tests/src/test/scala/cats/tests/ListWrapper.scala
index 2384c64d52a..2f081d77358 100644
--- a/tests/src/test/scala/cats/tests/ListWrapper.scala
+++ b/tests/src/test/scala/cats/tests/ListWrapper.scala
@@ -56,20 +56,20 @@ object ListWrapper {
     }
   }
 
-  val traverseEmpty: TraverseEmpty[ListWrapper] = {
-    val F = TraverseEmpty[List]
+  val traverseFilter: TraverseFilter[ListWrapper] = {
+    val F = TraverseFilter[List]
 
-    new TraverseEmpty[ListWrapper] {
+    new TraverseFilter[ListWrapper] {
       def traverse = ListWrapper.traverse
       def traverseFilter[G[_], A, B](fa: ListWrapper[A])(f: A => G[Option[B]])(implicit G: Applicative[G]): G[ListWrapper[B]] =
         G.map(F.traverseFilter(fa.list)(f))(ListWrapper.apply)
     }
   }
 
-  val functorEmpty: FunctorEmpty[ListWrapper] = {
-    val F = FunctorEmpty[List]
+  val functorFilter: FunctorFilter[ListWrapper] = {
+    val F = FunctorFilter[List]
 
-    new FunctorEmpty[ListWrapper] {
+    new FunctorFilter[ListWrapper] {
       def functor = ListWrapper.functor
       def mapFilter[A, B](fa: ListWrapper[A])(f: A => Option[B]): ListWrapper[B] =
         ListWrapper(F.mapFilter(fa.list)(f))
diff --git a/tests/src/test/scala/cats/tests/MapSuite.scala b/tests/src/test/scala/cats/tests/MapSuite.scala
index 591c7942a22..e05d19e5fac 100644
--- a/tests/src/test/scala/cats/tests/MapSuite.scala
+++ b/tests/src/test/scala/cats/tests/MapSuite.scala
@@ -2,7 +2,7 @@ package cats
 package tests
 
 
-import cats.laws.discipline.{FlatMapTests, FunctorEmptyTests, SemigroupalTests, SerializableTests, UnorderedTraverseTests, ComposeTests}
+import cats.laws.discipline.{FlatMapTests, FunctorFilterTests, SemigroupalTests, SerializableTests, UnorderedTraverseTests, ComposeTests}
 import cats.laws.discipline.arbitrary._
 import cats.arrow.Compose
 
@@ -18,8 +18,8 @@ class MapSuite extends CatsSuite {
   checkAll("Map[Int, Int] with Option", UnorderedTraverseTests[Map[Int, ?]].unorderedTraverse[Int, Int, Int, Option, Option])
   checkAll("UnorderedTraverse[Map[Int, ?]]", SerializableTests.serializable(UnorderedTraverse[Map[Int, ?]]))
 
-  checkAll("Map[Int, Int]", FunctorEmptyTests[Map[Int, ?]].functorEmpty[Int, Int, Int])
-  checkAll("FunctorEmpty[Map[Int, ?]]", SerializableTests.serializable(FunctorEmpty[Map[Int, ?]]))
+  checkAll("Map[Int, Int]", FunctorFilterTests[Map[Int, ?]].FunctorFilter[Int, Int, Int])
+  checkAll("FunctorFilter[Map[Int, ?]]", SerializableTests.serializable(FunctorFilter[Map[Int, ?]]))
 
   checkAll("Map[Int, Long]", ComposeTests[Map].compose[Int, Long, String, Double])
   checkAll("Compose[Map]", SerializableTests.serializable(Compose[Map]))
diff --git a/tests/src/test/scala/cats/tests/NestedSuite.scala b/tests/src/test/scala/cats/tests/NestedSuite.scala
index f5bd48f17eb..9b1802a9322 100644
--- a/tests/src/test/scala/cats/tests/NestedSuite.scala
+++ b/tests/src/test/scala/cats/tests/NestedSuite.scala
@@ -26,13 +26,13 @@ class NestedSuite extends CatsSuite {
   }
 
   {
-    // TraverseEmpty composition
-    implicit val instance = ListWrapper.traverseEmpty
+    // TraverseFilter composition
+    implicit val instance = ListWrapper.traverseFilter
     implicit val traverseInstance = ListWrapper.traverse
     checkAll("Nested[ListWrapper, ListWrapper]",
-      TraverseEmptyTests[Nested[ListWrapper, ListWrapper, ?]].traverseEmpty[Int, Int, Int])
-    checkAll("TraverseEmpty[Nested[ListWrapper, ListWrapper, ?]]",
-      SerializableTests.serializable(TraverseEmpty[Nested[ListWrapper, ListWrapper, ?]]))
+      TraverseFilterTests[Nested[ListWrapper, ListWrapper, ?]].traverseFilter[Int, Int, Int])
+    checkAll("TraverseFilter[Nested[ListWrapper, ListWrapper, ?]]",
+      SerializableTests.serializable(TraverseFilter[Nested[ListWrapper, ListWrapper, ?]]))
   }
 
   {
diff --git a/tests/src/test/scala/cats/tests/OptionSuite.scala b/tests/src/test/scala/cats/tests/OptionSuite.scala
index 8604b3b7d92..ae36f201298 100644
--- a/tests/src/test/scala/cats/tests/OptionSuite.scala
+++ b/tests/src/test/scala/cats/tests/OptionSuite.scala
@@ -21,8 +21,8 @@ class OptionSuite extends CatsSuite {
   checkAll("Option[Int] with Option", TraverseTests[Option].traverse[Int, Int, Int, Int, Option, Option])
   checkAll("Traverse[Option]", SerializableTests.serializable(Traverse[Option]))
 
-  checkAll("Option[Int] with Option", TraverseEmptyTests[Option].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[Option]", SerializableTests.serializable(TraverseEmpty[Option]))
+  checkAll("Option[Int] with Option", TraverseFilterTests[Option].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[Option]", SerializableTests.serializable(TraverseFilter[Option]))
 
   checkAll("Option with Unit", MonadErrorTests[Option, Unit].monadError[Int, Int, Int])
   checkAll("MonadError[Option, Unit]", SerializableTests.serializable(MonadError[Option, Unit]))
diff --git a/tests/src/test/scala/cats/tests/OptionTSuite.scala b/tests/src/test/scala/cats/tests/OptionTSuite.scala
index d1223280be5..bf34daa456f 100644
--- a/tests/src/test/scala/cats/tests/OptionTSuite.scala
+++ b/tests/src/test/scala/cats/tests/OptionTSuite.scala
@@ -10,7 +10,7 @@ class OptionTSuite extends CatsSuite {
   implicit val iso = SemigroupalTests.Isomorphisms.invariant[OptionT[ListWrapper, ?]](OptionT.catsDataFunctorForOptionT(ListWrapper.functor))
 
   checkAll("OptionT[Eval, ?]", DeferTests[OptionT[Eval, ?]].defer[Int])
-  checkAll("OptionT[Eval, ?]", FunctorEmptyTests[OptionT[Eval, ?]].functorEmpty[Int, Int, Int])
+  checkAll("OptionT[Eval, ?]", FunctorFilterTests[OptionT[Eval, ?]].functorFilter[Int, Int, Int])
 
 
   {
diff --git a/tests/src/test/scala/cats/tests/SortedMapSuite.scala b/tests/src/test/scala/cats/tests/SortedMapSuite.scala
index 13283fe6623..5c4af5c6fd1 100644
--- a/tests/src/test/scala/cats/tests/SortedMapSuite.scala
+++ b/tests/src/test/scala/cats/tests/SortedMapSuite.scala
@@ -3,7 +3,7 @@ package tests
 
 import cats.kernel.CommutativeMonoid
 import cats.kernel.laws.discipline.{CommutativeMonoidTests, HashTests, MonoidTests}
-import cats.laws.discipline.{FlatMapTests, SemigroupalTests, SerializableTests, TraverseEmptyTests, TraverseTests}
+import cats.laws.discipline.{FlatMapTests, SemigroupalTests, SerializableTests, TraverseFilterTests, TraverseTests}
 import cats.laws.discipline.arbitrary._
 
 import scala.collection.immutable.SortedMap
@@ -20,8 +20,8 @@ class SortedMapSuite extends CatsSuite {
   checkAll("SortedMap[Int, Int] with Option", TraverseTests[SortedMap[Int, ?]].traverse[Int, Int, Int, Int, Option, Option])
   checkAll("Traverse[SortedMap[Int, ?]]", SerializableTests.serializable(Traverse[SortedMap[Int, ?]]))
 
-  checkAll("SortedMap[Int, Int]", TraverseEmptyTests[SortedMap[Int, ?]].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[SortedMap[Int, ?]]", SerializableTests.serializable(TraverseEmpty[SortedMap[Int, ?]]))
+  checkAll("SortedMap[Int, Int]", TraverseFilterTests[SortedMap[Int, ?]].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[SortedMap[Int, ?]]", SerializableTests.serializable(TraverseFilter[SortedMap[Int, ?]]))
 
   test("show isn't empty and is formatted as expected") {
     forAll { (map: SortedMap[Int, String]) =>
diff --git a/tests/src/test/scala/cats/tests/StreamSuite.scala b/tests/src/test/scala/cats/tests/StreamSuite.scala
index 75a7a5d1beb..25f7c1bb4df 100644
--- a/tests/src/test/scala/cats/tests/StreamSuite.scala
+++ b/tests/src/test/scala/cats/tests/StreamSuite.scala
@@ -1,7 +1,7 @@
 package cats
 package tests
 
-import cats.laws.discipline.{AlternativeTests, CoflatMapTests, CommutativeApplyTests, MonadTests, SemigroupalTests, SerializableTests, TraverseEmptyTests, TraverseTests}
+import cats.laws.discipline.{AlternativeTests, CoflatMapTests, CommutativeApplyTests, MonadTests, SemigroupalTests, SerializableTests, TraverseFilterTests, TraverseTests}
 import cats.data.ZipStream
 import cats.laws.discipline.arbitrary._
 
@@ -21,8 +21,8 @@ class StreamSuite extends CatsSuite {
   checkAll("Stream[Int] with Option", TraverseTests[Stream].traverse[Int, Int, Int, Set[Int], Option, Option])
   checkAll("Traverse[Stream]", SerializableTests.serializable(Traverse[Stream]))
 
-  checkAll("Stream[Int]", TraverseEmptyTests[Stream].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[Stream]", SerializableTests.serializable(TraverseEmpty[Stream]))
+  checkAll("Stream[Int]", TraverseFilterTests[Stream].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[Stream]", SerializableTests.serializable(TraverseFilter[Stream]))
 
   // Can't test applicative laws as they don't terminate
   checkAll("ZipStream[Int]", CommutativeApplyTests[ZipStream].apply[Int, Int, Int])
diff --git a/tests/src/test/scala/cats/tests/VectorSuite.scala b/tests/src/test/scala/cats/tests/VectorSuite.scala
index aff1464dddd..1d9562f8fa7 100644
--- a/tests/src/test/scala/cats/tests/VectorSuite.scala
+++ b/tests/src/test/scala/cats/tests/VectorSuite.scala
@@ -2,7 +2,7 @@ package cats
 package tests
 
 import cats.data.{NonEmptyVector, ZipVector}
-import cats.laws.discipline.{AlternativeTests, CoflatMapTests, CommutativeApplyTests, MonadTests, SemigroupalTests, SerializableTests, TraverseEmptyTests, TraverseTests}
+import cats.laws.discipline.{AlternativeTests, CoflatMapTests, CommutativeApplyTests, MonadTests, SemigroupalTests, SerializableTests, TraverseFilterTests, TraverseTests}
 import cats.laws.discipline.arbitrary._
 
 class VectorSuite extends CatsSuite {
@@ -21,8 +21,8 @@ class VectorSuite extends CatsSuite {
   checkAll("Vector[Int]", MonadTests[Vector].monad[Int, Int, Int])
   checkAll("Monad[Vector]", SerializableTests.serializable(Monad[Vector]))
 
-  checkAll("Vector[Int]", TraverseEmptyTests[Vector].traverseEmpty[Int, Int, Int])
-  checkAll("TraverseEmpty[Vector]", SerializableTests.serializable(TraverseEmpty[Vector]))
+  checkAll("Vector[Int]", TraverseFilterTests[Vector].traverseFilter[Int, Int, Int])
+  checkAll("TraverseFilter[Vector]", SerializableTests.serializable(TraverseFilter[Vector]))
 
   checkAll("ZipVector[Int]", CommutativeApplyTests[ZipVector].commutativeApply[Int, Int, Int])