diff --git a/core/src/main/scala-2.13+/cats/instances/lazyList.scala b/core/src/main/scala-2.13+/cats/instances/lazyList.scala
index 807b928dba..0cfc3f414c 100644
--- a/core/src/main/scala-2.13+/cats/instances/lazyList.scala
+++ b/core/src/main/scala-2.13+/cats/instances/lazyList.scala
@@ -182,9 +182,9 @@ trait LazyListInstances extends cats.kernel.instances.LazyListInstances {
       def applicative: Applicative[ZipLazyList] = ZipLazyList.catsDataAlternativeForZipLazyList
 
       def sequential: ZipLazyList ~> LazyList =
-        new (ZipLazyList ~> LazyList) { def apply[A](a: ZipLazyList[A]): LazyList[A] = a.value }
+        new (ZipLazyList ~> LazyList) { def apply[B](zll: ZipLazyList[B]): LazyList[B] = zll.value }
 
       def parallel: LazyList ~> ZipLazyList =
-        new (LazyList ~> ZipLazyList) { def apply[A](v: LazyList[A]): ZipLazyList[A] = new ZipLazyList(v) }
+        new (LazyList ~> ZipLazyList) { def apply[B](ll: LazyList[B]): ZipLazyList[B] = new ZipLazyList(ll) }
     }
 }
diff --git a/free/src/main/scala/cats/free/Free.scala b/free/src/main/scala/cats/free/Free.scala
index 069210f6e6..a8c759be0f 100644
--- a/free/src/main/scala/cats/free/Free.scala
+++ b/free/src/main/scala/cats/free/Free.scala
@@ -29,7 +29,7 @@ sealed abstract class Free[S[_], A] extends Product with Serializable {
    */
   final def mapK[T[_]](f: S ~> T): Free[T, A] =
     foldMap[Free[T, *]] { // this is safe because Free is stack safe
-      new FunctionK[S, Free[T, *]] { def apply[A](fa: S[A]): Free[T, A] = Suspend(f(fa)) }
+      new FunctionK[S, Free[T, *]] { def apply[B](sb: S[B]): Free[T, B] = Suspend(f(sb)) }
     }
 
   /**
@@ -181,10 +181,10 @@ sealed abstract class Free[S[_], A] extends Product with Serializable {
    *}}}
    */
   final def inject[G[_]](implicit ev: InjectK[S, G]): Free[G, A] =
-    mapK(new (S ~> G) { def apply[A](a: S[A]): G[A] = ev.inj(a) })
+    mapK(new (S ~> G) { def apply[B](sb: S[B]): G[B] = ev.inj(sb) })
 
   final def toFreeT[G[_]: Applicative]: FreeT[S, G, A] =
-    foldMap[FreeT[S, G, *]](new (S ~> FreeT[S, G, *]) { def apply[A](a: S[A]): FreeT[S, G, A] = FreeT.liftF(a) })
+    foldMap[FreeT[S, G, *]](new (S ~> FreeT[S, G, *]) { def apply[B](sb: S[B]): FreeT[S, G, B] = FreeT.liftF(sb) })
 
   override def toString: String =
     "Free(...)"
diff --git a/free/src/main/scala/cats/free/FreeApplicative.scala b/free/src/main/scala/cats/free/FreeApplicative.scala
index adfee32303..efbfa80977 100644
--- a/free/src/main/scala/cats/free/FreeApplicative.scala
+++ b/free/src/main/scala/cats/free/FreeApplicative.scala
@@ -141,7 +141,7 @@ sealed abstract class FreeApplicative[F[_], A] extends Product with Serializable
    */
   final def compile[G[_]](f: F ~> G): FA[G, A] =
     foldMap[FA[G, *]] {
-      new FunctionK[F, FA[G, *]] { def apply[A](fa: F[A]): FA[G, A] = lift(f(fa)) }
+      new FunctionK[F, FA[G, *]] { def apply[B](fb: F[B]): FA[G, B] = lift(f(fb)) }
     }
 
   /**
@@ -154,13 +154,13 @@ sealed abstract class FreeApplicative[F[_], A] extends Product with Serializable
   /** Interpret this algebra into a Monoid. */
   final def analyze[M: Monoid](f: FunctionK[F, λ[α => M]]): M =
     foldMap[Const[M, *]](
-      new FunctionK[F, Const[M, *]] { def apply[A](x: F[A]): Const[M, A] = Const(f(x)) }
+      new FunctionK[F, Const[M, *]] { def apply[B](fb: F[B]): Const[M, B] = Const(f(fb)) }
     ).getConst
 
   /** Compile this FreeApplicative algebra into a Free algebra. */
   final def monad: Free[F, A] =
     foldMap[Free[F, *]] {
-      new FunctionK[F, Free[F, *]] { def apply[A](fa: F[A]): Free[F, A] = Free.liftF(fa) }
+      new FunctionK[F, Free[F, *]] { def apply[B](fb: F[B]): Free[F, B] = Free.liftF(fb) }
     }
 
   override def toString: String = "FreeApplicative(...)"
diff --git a/free/src/main/scala/cats/free/FreeInvariantMonoidal.scala b/free/src/main/scala/cats/free/FreeInvariantMonoidal.scala
index 15834af55d..469da479db 100644
--- a/free/src/main/scala/cats/free/FreeInvariantMonoidal.scala
+++ b/free/src/main/scala/cats/free/FreeInvariantMonoidal.scala
@@ -28,13 +28,13 @@ sealed abstract class FreeInvariantMonoidal[F[_], A] extends Product with Serial
   /** Interpret this algebra into another InvariantMonoidal */
   final def compile[G[_]](f: FunctionK[F, G]): FA[G, A] =
     foldMap[FA[G, *]] {
-      new FunctionK[F, FA[G, *]] { def apply[A](fa: F[A]): FA[G, A] = lift(f(fa)) }
+      new FunctionK[F, FA[G, *]] { def apply[B](fb: F[B]): FA[G, B] = lift(f(fb)) }
     }
 
   /** Interpret this algebra into a Monoid */
   final def analyze[M: Monoid](f: FunctionK[F, λ[α => M]]): M =
     foldMap[Const[M, *]](
-      new FunctionK[F, Const[M, *]] { def apply[A](x: F[A]): Const[M, A] = Const(f(x)) }
+      new FunctionK[F, Const[M, *]] { def apply[B](fb: F[B]): Const[M, B] = Const(f(fb)) }
     ).getConst
 }