diff --git a/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala b/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala
index 5591b8abded..218ab50a706 100644
--- a/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala
+++ b/core/src/main/scala-2.13+/cats/data/NonEmptyLazyList.scala
@@ -213,7 +213,7 @@ class NonEmptyLazyListOps[A](private val value: NonEmptyLazyList[A])
    * Tests if some element is contained in this NonEmptyLazyList
    */
   final def contains(a: A)(implicit A: Eq[A]): Boolean =
-    toLazyList.contains(a)
+    exists(A.eqv(a, _))
 
   /**
    * Tests whether a predicate holds for all elements
diff --git a/core/src/main/scala-2.13+/cats/instances/stream.scala b/core/src/main/scala-2.13+/cats/instances/stream.scala
index ad01c35758b..cc8687100ed 100644
--- a/core/src/main/scala-2.13+/cats/instances/stream.scala
+++ b/core/src/main/scala-2.13+/cats/instances/stream.scala
@@ -104,7 +104,7 @@ trait StreamInstances extends cats.kernel.instances.StreamInstances {
               case Left(a) #:: tail =>
                 stack = fn(a) #::: tail
                 advance()
-              case empty =>
+              case _ =>
                 state = Right(None)
             }
 
diff --git a/core/src/main/scala-2/src/main/scala/cats/arrow/FunctionKMacros.scala b/core/src/main/scala-2/src/main/scala/cats/arrow/FunctionKMacros.scala
index 89dd8846bd4..51ed68ee7f6 100644
--- a/core/src/main/scala-2/src/main/scala/cats/arrow/FunctionKMacros.scala
+++ b/core/src/main/scala-2/src/main/scala/cats/arrow/FunctionKMacros.scala
@@ -22,7 +22,6 @@
 package cats
 package arrow
 
-import scala.language.experimental.macros
 import scala.reflect.macros.blackbox
 
 private[arrow] class FunctionKMacroMethods {
diff --git a/core/src/main/scala-2/src/main/scala/cats/compat/targetName.scala b/core/src/main/scala-2/src/main/scala/cats/compat/targetName.scala
index 44e0e795aaa..50ef43c2594 100644
--- a/core/src/main/scala-2/src/main/scala/cats/compat/targetName.scala
+++ b/core/src/main/scala-2/src/main/scala/cats/compat/targetName.scala
@@ -22,6 +22,7 @@
 package cats.compat
 
 import scala.annotation.Annotation
+import scala.annotation.nowarn
 
 // compat dummy so we can use targetName on scala 3 to get out of bincompat pickles
-private[cats] class targetName(dummy: String) extends Annotation
+private[cats] class targetName(@nowarn("cat=unused-params") dummy: String) extends Annotation
diff --git a/core/src/main/scala/cats/ApplicativeError.scala b/core/src/main/scala/cats/ApplicativeError.scala
index 847930d56e7..4c7eb925cb0 100644
--- a/core/src/main/scala/cats/ApplicativeError.scala
+++ b/core/src/main/scala/cats/ApplicativeError.scala
@@ -25,6 +25,7 @@ import cats.ApplicativeError.CatchOnlyPartiallyApplied
 import cats.data.{EitherT, Validated}
 import cats.data.Validated.{Invalid, Valid}
 
+import scala.annotation.nowarn
 import scala.reflect.ClassTag
 import scala.util.control.NonFatal
 import scala.util.{Failure, Success, Try}
@@ -353,7 +354,13 @@ object ApplicativeError {
 
   final private[cats] class CatchOnlyPartiallyApplied[T, F[_], E](private val F: ApplicativeError[F, E])
       extends AnyVal {
-    def apply[A](f: => A)(implicit CT: ClassTag[T], NT: NotNull[T], ev: Throwable <:< E): F[A] =
+
+    def apply[A](f: => A)(implicit
+      CT: ClassTag[T],
+      @nowarn("cat=unused-params")
+      NT: NotNull[T],
+      ev: Throwable <:< E
+    ): F[A] =
       try {
         F.pure(f)
       } catch {
diff --git a/core/src/main/scala/cats/TraverseFilter.scala b/core/src/main/scala/cats/TraverseFilter.scala
index 76628ac4088..d96eeaf7066 100644
--- a/core/src/main/scala/cats/TraverseFilter.scala
+++ b/core/src/main/scala/cats/TraverseFilter.scala
@@ -124,7 +124,12 @@ trait TraverseFilter[F[_]] extends FunctorFilter[F] {
 
   /**
    * Removes duplicate elements from a list, keeping only the first occurrence.
-   * This is usually faster than ordDistinct, especially for things that have a slow comparion (like String).
+   * This is usually faster than ordDistinct, especially for things that have a slow comparison (like String).
+   * 
+   * @note the passed `Hash` typeclass is not currently in use.
+   * @todo replace `HashSet` from Scala library with one that can make use of the `Hash` typeclass
+   *       instead of the Java's `hashCode` method. Consider a candidate implementation in
+   *       [[https://github.com/typelevel/cats/pull/4185 PR#4185]].
    */
   def hashDistinct[A](fa: F[A])(implicit H: Hash[A]): F[A] =
     traverseFilter[State[HashSet[A], *], A, A](fa)(a =>
diff --git a/core/src/main/scala/cats/data/Const.scala b/core/src/main/scala/cats/data/Const.scala
index 28626fa51a4..d6722f06910 100644
--- a/core/src/main/scala/cats/data/Const.scala
+++ b/core/src/main/scala/cats/data/Const.scala
@@ -23,6 +23,7 @@ package cats
 package data
 
 import cats.kernel.{CommutativeMonoid, CommutativeSemigroup, LowerBounded, UpperBounded}
+import scala.annotation.nowarn
 
 /**
  * [[Const]] is a phantom type, it does not contain a value of its second type parameter `B`
@@ -39,7 +40,7 @@ final case class Const[A, B](getConst: A) {
   def combine(that: Const[A, B])(implicit A: Semigroup[A]): Const[A, B] =
     Const(A.combine(getConst, that.getConst))
 
-  def traverse[F[_], C](f: B => F[C])(implicit F: Applicative[F]): F[Const[A, C]] =
+  def traverse[F[_], C](@nowarn("cat=unused-params") f: B => F[C])(implicit F: Applicative[F]): F[Const[A, C]] =
     F.pure(retag[C])
 
   def ===(that: Const[A, B])(implicit A: Eq[A]): Boolean =
diff --git a/core/src/main/scala/cats/data/EitherT.scala b/core/src/main/scala/cats/data/EitherT.scala
index bc59e634406..69932adccc2 100644
--- a/core/src/main/scala/cats/data/EitherT.scala
+++ b/core/src/main/scala/cats/data/EitherT.scala
@@ -986,7 +986,6 @@ abstract private[data] class EitherTInstances extends EitherTInstances1 {
       type F[x] = Nested[P.F, Validated[E, *], x]
 
       implicit val monadM: Monad[M] = P.monad
-      implicit val monadEither: Monad[Either[E, *]] = cats.instances.either.catsStdInstancesForEither
 
       def applicative: Applicative[Nested[P.F, Validated[E, *], *]] =
         cats.data.Nested.catsDataApplicativeForNested(P.applicative, Validated.catsDataApplicativeErrorForValidated)
@@ -1017,7 +1016,6 @@ abstract private[data] class EitherTInstances extends EitherTInstances1 {
       type F[x] = Nested[P.F, Either[E, *], x]
 
       implicit val monadM: Monad[M] = P.monad
-      implicit val monadEither: Monad[Either[E, *]] = cats.instances.either.catsStdInstancesForEither
 
       def applicative: Applicative[Nested[P.F, Either[E, *], *]] =
         cats.data.Nested.catsDataApplicativeForNested(P.applicative, implicitly)
@@ -1082,7 +1080,6 @@ abstract private[data] class EitherTInstances1 extends EitherTInstances2 {
       type F[x] = Nested[M, Validated[E, *], x]
 
       implicit val appValidated: Applicative[Validated[E, *]] = Validated.catsDataApplicativeErrorForValidated
-      implicit val monadEither: Monad[Either[E, *]] = cats.instances.either.catsStdInstancesForEither
 
       def applicative: Applicative[Nested[M, Validated[E, *], *]] =
         cats.data.Nested.catsDataApplicativeForNested[M, Validated[E, *]]
@@ -1154,14 +1151,14 @@ private[data] trait EitherTSemigroupK[F[_], L] extends SemigroupK[EitherT[F, L,
   implicit val F: Monad[F]
   def combineK[A](x: EitherT[F, L, A], y: EitherT[F, L, A]): EitherT[F, L, A] =
     EitherT(F.flatMap(x.value) {
-      case l @ Left(_)  => y.value
-      case r @ Right(_) => F.pure(r)
+      case r: Right[L, A] => F.pure(r)
+      case _              => y.value
     })
 
   override def combineKEval[A](x: EitherT[F, L, A], y: Eval[EitherT[F, L, A]]): Eval[EitherT[F, L, A]] =
     Eval.now(EitherT(F.flatMap(x.value) {
-      case l @ Left(_)  => y.value.value
-      case r @ Right(_) => F.pure(r: Either[L, A])
+      case r: Right[L, A] => F.pure(r)
+      case _              => y.value.value
     }))
 }
 
diff --git a/core/src/main/scala/cats/data/Func.scala b/core/src/main/scala/cats/data/Func.scala
index 6ca7327297f..7d274ee7ffd 100644
--- a/core/src/main/scala/cats/data/Func.scala
+++ b/core/src/main/scala/cats/data/Func.scala
@@ -113,7 +113,7 @@ sealed private[data] trait FuncApply[F[_], C] extends Apply[λ[α => Func[F, C,
 sealed private[data] trait FuncApplicative[F[_], C] extends Applicative[λ[α => Func[F, C, α]]] with FuncApply[F, C] {
   def F: Applicative[F]
   def pure[A](a: A): Func[F, C, A] =
-    Func.func(c => F.pure(a))
+    Func.func(_ => F.pure(a))
 }
 
 /**
@@ -167,5 +167,5 @@ sealed private[data] trait AppFuncApplicative[F[_], C] extends Applicative[λ[α
   override def product[A, B](fa: AppFunc[F, C, A], fb: AppFunc[F, C, B]): AppFunc[F, C, (A, B)] =
     Func.appFunc[F, C, (A, B)](c => F.product(fa.run(c), fb.run(c)))(F)
   def pure[A](a: A): AppFunc[F, C, A] =
-    Func.appFunc[F, C, A](c => F.pure(a))(F)
+    Func.appFunc[F, C, A](_ => F.pure(a))(F)
 }
diff --git a/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala b/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala
index 26b684ef540..de542ff40af 100644
--- a/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala
+++ b/core/src/main/scala/cats/data/IndexedReaderWriterStateT.scala
@@ -246,7 +246,7 @@ final class IndexedReaderWriterStateT[F[_], E, L, SA, SB, A](val runF: F[(E, SA)
    * Inspect a value from the input state, without modifying the state.
    */
   def inspect[B](f: SB => B)(implicit F: Functor[F]): IndexedReaderWriterStateT[F, E, L, SA, SB, B] =
-    transform { (l, sb, a) =>
+    transform { (l, sb, _) =>
       (l, sb, f(sb))
     }
 
@@ -287,7 +287,7 @@ final class IndexedReaderWriterStateT[F[_], E, L, SA, SB, A](val runF: F[(E, SA)
    * Retrieve the value written to the log.
    */
   def written(implicit F: Functor[F]): IndexedReaderWriterStateT[F, E, L, SA, SB, L] =
-    transform { (l, sb, a) =>
+    transform { (l, sb, _) =>
       (l, sb, l)
     }
 
@@ -555,7 +555,11 @@ abstract private[data] class RWSFunctions {
   /**
    * Return `a` and an empty log without modifying the input state.
    */
-  def apply[E, L: Monoid, S, A](f: (E, S) => (L, S, A)): ReaderWriterState[E, L, S, A] =
+  def apply[E, L, S, A](f: (E, S) => (L, S, A)): ReaderWriterState[E, L, S, A] =
+    ReaderWriterStateT.applyF(Now((e, s) => Now(f(e, s))))
+
+  @deprecated("2.8.0", "Use apply without the Monoid constraint")
+  protected def apply[E, L: Monoid, S, A](f: (E, S) => (L, S, A)): ReaderWriterState[E, L, S, A] =
     ReaderWriterStateT.applyF(Now((e, s) => Now(f(e, s))))
 
   /**
diff --git a/core/src/main/scala/cats/data/IndexedStateT.scala b/core/src/main/scala/cats/data/IndexedStateT.scala
index 92ff65a2f58..683693785d3 100644
--- a/core/src/main/scala/cats/data/IndexedStateT.scala
+++ b/core/src/main/scala/cats/data/IndexedStateT.scala
@@ -483,7 +483,7 @@ sealed abstract private[data] class IndexedStateTContravariantMonoidal[F[_], S]
   implicit def G: Applicative[F]
 
   override def unit: IndexedStateT[F, S, S, Unit] =
-    IndexedStateT.applyF(G.pure((s: S) => F.trivial[(S, Unit)]))
+    IndexedStateT.applyF(G.pure((_: S) => F.trivial[(S, Unit)]))
 
   override def contramap[A, B](fa: IndexedStateT[F, S, S, A])(f: B => A): IndexedStateT[F, S, S, B] =
     contramap2(fa, trivial)(((a: A) => (a, a)).compose(f))
diff --git a/core/src/main/scala/cats/data/Ior.scala b/core/src/main/scala/cats/data/Ior.scala
index 9c6def13d08..1b800e18a97 100644
--- a/core/src/main/scala/cats/data/Ior.scala
+++ b/core/src/main/scala/cats/data/Ior.scala
@@ -775,9 +775,9 @@ sealed abstract class Ior[+A, +B] extends Product with Serializable {
 
   final def ===[AA >: A, BB >: B](that: AA Ior BB)(implicit AA: Eq[AA], BB: Eq[BB]): Boolean =
     fold(
-      a => that.fold(a2 => AA.eqv(a, a2), b2 => false, (a2, b2) => false),
-      b => that.fold(a2 => false, b2 => BB.eqv(b, b2), (a2, b2) => false),
-      (a, b) => that.fold(a2 => false, b2 => false, (a2, b2) => AA.eqv(a, a2) && BB.eqv(b, b2))
+      a => that.fold(a2 => AA.eqv(a, a2), _ => false, (_, _) => false),
+      b => that.fold(_ => false, b2 => BB.eqv(b, b2), (_, _) => false),
+      (a, b) => that.fold(_ => false, _ => false, (a2, b2) => AA.eqv(a, a2) && BB.eqv(b, b2))
     )
 
   final def compare[AA >: A, BB >: B](that: AA Ior BB)(implicit AA: Order[AA], BB: Order[BB]): Int =
@@ -929,9 +929,9 @@ sealed abstract private[data] class IorInstances extends IorInstances0 {
               }
             case Ior.Left(e1) =>
               ff match {
-                case Ior.Right(f)    => Ior.Left(e1)
-                case Ior.Both(e2, f) => Ior.Left(E.combine(e2, e1))
+                case Ior.Both(e2, _) => Ior.Left(E.combine(e2, e1))
                 case Ior.Left(e2)    => Ior.Left(E.combine(e2, e1))
+                case _               => Ior.Left(e1)
               }
           }
       }
diff --git a/core/src/main/scala/cats/data/NonEmptySet.scala b/core/src/main/scala/cats/data/NonEmptySet.scala
index 9b6526d2c27..71ff8721490 100644
--- a/core/src/main/scala/cats/data/NonEmptySet.scala
+++ b/core/src/main/scala/cats/data/NonEmptySet.scala
@@ -428,7 +428,7 @@ sealed abstract private[data] class NonEmptySetInstances extends NonEmptySetInst
 }
 
 sealed abstract private[data] class NonEmptySetInstances0 extends NonEmptySetInstances1 {
-  implicit def catsDataHashForNonEmptySet[A: Order: Hash]: Hash[NonEmptySet[A]] =
+  implicit def catsDataHashForNonEmptySet[A: Hash]: Hash[NonEmptySet[A]] =
     Hash[SortedSet[A]].asInstanceOf[Hash[NonEmptySet[A]]]
 }
 
diff --git a/core/src/main/scala/cats/data/RepresentableStore.scala b/core/src/main/scala/cats/data/RepresentableStore.scala
index 867e1dff40d..2a7efd016ae 100644
--- a/core/src/main/scala/cats/data/RepresentableStore.scala
+++ b/core/src/main/scala/cats/data/RepresentableStore.scala
@@ -95,19 +95,25 @@ final case class RepresentableStore[F[_], S, A](fa: F[A], index: S)(implicit R:
 
 object RepresentableStore {
 
-  implicit def catsDataRepresentableStoreComonad[F[_], S](implicit
-    R: Representable[F]
-  ): Comonad[RepresentableStore[F, S, *]] =
-    new Comonad[RepresentableStore[F, S, *]] {
-      override def extract[B](x: RepresentableStore[F, S, B]): B =
-        x.extract
-
-      override def coflatMap[A, B](
-        fa: RepresentableStore[F, S, A]
-      )(f: RepresentableStore[F, S, A] => B): RepresentableStore[F, S, B] =
-        fa.coflatten.map(f)
-
-      override def map[A, B](fa: RepresentableStore[F, S, A])(f: A => B): RepresentableStore[F, S, B] =
-        fa.map(f)
-    }
+  implicit def catsDataRepresentableStoreComonadBinCompat[F[_], S]: Comonad[RepresentableStore[F, S, *]] =
+    new RepresentableStoreComonad[F, S]
+
+  @deprecated("Use catsDataRepresentableStoreComonadBinCompat instead", "2.8.0")
+  def catsDataRepresentableStoreComonad[F[_], S](R: Representable[F]): Comonad[RepresentableStore[F, S, *]] =
+    new RepresentableStoreComonad[F, S]
+
+  final private class RepresentableStoreComonad[F[_], S] private[RepresentableStore]
+      extends Comonad[RepresentableStore[F, S, *]] {
+
+    override def extract[B](x: RepresentableStore[F, S, B]): B =
+      x.extract
+
+    override def coflatMap[A, B](
+      fa: RepresentableStore[F, S, A]
+    )(f: RepresentableStore[F, S, A] => B): RepresentableStore[F, S, B] =
+      fa.coflatten.map(f)
+
+    override def map[A, B](fa: RepresentableStore[F, S, A])(f: A => B): RepresentableStore[F, S, B] =
+      fa.map(f)
+  }
 }
diff --git a/core/src/main/scala/cats/data/Validated.scala b/core/src/main/scala/cats/data/Validated.scala
index 847b9795369..ce3311dc587 100644
--- a/core/src/main/scala/cats/data/Validated.scala
+++ b/core/src/main/scala/cats/data/Validated.scala
@@ -25,6 +25,7 @@ package data
 import cats.data.Validated.{Invalid, Valid}
 import cats.kernel.CommutativeSemigroup
 
+import scala.annotation.nowarn
 import scala.reflect.ClassTag
 import scala.util.{Failure, Success, Try}
 
@@ -859,7 +860,11 @@ object Validated extends ValidatedInstances with ValidatedFunctions with Validat
   final private[data] class CatchOnlyPartiallyApplied[T](private val dummy: Boolean = true) extends AnyVal {
     /* Note: the NT parameter is not referenced at runtime, but serves a compile-time role.
      * See https://github.com/typelevel/cats/pull/1867/files#r138381991 for details. */
-    def apply[A](f: => A)(implicit T: ClassTag[T], NT: NotNull[T]): Validated[T, A] =
+    def apply[A](f: => A)(implicit
+      T: ClassTag[T],
+      @nowarn("cat=unused-params")
+      NT: NotNull[T]
+    ): Validated[T, A] =
       try {
         valid(f)
       } catch {
@@ -894,13 +899,13 @@ sealed abstract private[data] class ValidatedInstances extends ValidatedInstance
         fa match {
           case Invalid(e) =>
             fb match {
-              case Invalid(e2) => Invalid(Semigroup[E].combine(e, e2))
               case Valid(b)    => Valid(f(Ior.right(b)))
+              case Invalid(e2) => Invalid(Semigroup[E].combine(e, e2))
             }
           case Valid(a) =>
             fb match {
-              case Invalid(e) => Valid(f(Ior.left(a)))
-              case Valid(b)   => Valid(f(Ior.both(a, b)))
+              case Valid(b) => Valid(f(Ior.both(a, b)))
+              case _        => Valid(f(Ior.left(a)))
             }
         }
     }
diff --git a/core/src/main/scala/cats/instances/either.scala b/core/src/main/scala/cats/instances/either.scala
index 70c3b0ea718..26ad1f4c122 100644
--- a/core/src/main/scala/cats/instances/either.scala
+++ b/core/src/main/scala/cats/instances/either.scala
@@ -189,15 +189,15 @@ trait EitherInstances extends cats.kernel.instances.EitherInstances {
 
       override def alignWith[B, C, D](fb: Either[A, B], fc: Either[A, C])(f: Ior[B, C] => D): Either[A, D] =
         fb match {
-          case left @ Left(a) =>
+          case left: Left[A, B] =>
             fc match {
-              case Left(_)  => left.rightCast[D]
               case Right(c) => Right(f(Ior.right(c)))
+              case _        => left.rightCast[D]
             }
           case Right(b) =>
             fc match {
-              case Left(a)  => Right(f(Ior.left(b)))
               case Right(c) => Right(f(Ior.both(b, c)))
+              case _        => Right(f(Ior.left(b)))
             }
         }
 
diff --git a/core/src/main/scala/cats/instances/map.scala b/core/src/main/scala/cats/instances/map.scala
index 4eefa6a8ac7..9c3e1867df0 100644
--- a/core/src/main/scala/cats/instances/map.scala
+++ b/core/src/main/scala/cats/instances/map.scala
@@ -79,7 +79,7 @@ trait MapInstances extends cats.kernel.instances.MapInstances {
         fa.flatMap { case (k, a) => f(a).get(k).map((k, _)) }
 
       def unorderedFoldMap[A, B: CommutativeMonoid](fa: Map[K, A])(f: (A) => B) =
-        fa.foldLeft(Monoid[B].empty) { case (b, (k, a)) => Monoid[B].combine(b, f(a)) }
+        fa.foldLeft(Monoid[B].empty) { case (b, (_, a)) => Monoid[B].combine(b, f(a)) }
 
       def tailRecM[A, B](a: A)(f: A => Map[K, Either[A, B]]): Map[K, B] = {
         val bldr = Map.newBuilder[K, B]
diff --git a/core/src/main/scala/cats/instances/sortedMap.scala b/core/src/main/scala/cats/instances/sortedMap.scala
index 6454ffb6867..d6d1b867596 100644
--- a/core/src/main/scala/cats/instances/sortedMap.scala
+++ b/core/src/main/scala/cats/instances/sortedMap.scala
@@ -201,10 +201,7 @@ class SortedMapEq[K, V](implicit V: Eq[V], O: Order[K]) extends cats.kernel.inst
 @deprecated("Use cats.kernel.instances.SortedMapCommutativeMonoid", "2.0.0-RC2")
 class SortedMapCommutativeMonoid[K, V](implicit V: CommutativeSemigroup[V], O: Order[K])
     extends SortedMapMonoid[K, V]
-    with CommutativeMonoid[SortedMap[K, V]] {
-  private[this] val underlying: CommutativeMonoid[SortedMap[K, V]] =
-    new cats.kernel.instances.SortedMapCommutativeMonoid[K, V]
-}
+    with CommutativeMonoid[SortedMap[K, V]]
 
 @deprecated("Use cats.kernel.instances.SortedMapMonoid", "2.0.0-RC2")
 class SortedMapMonoid[K, V](implicit V: Semigroup[V], O: Order[K]) extends cats.kernel.instances.SortedMapMonoid[K, V]
diff --git a/core/src/main/scala/cats/syntax/applicativeError.scala b/core/src/main/scala/cats/syntax/applicativeError.scala
index ff12673bb6b..e81baaeeca3 100644
--- a/core/src/main/scala/cats/syntax/applicativeError.scala
+++ b/core/src/main/scala/cats/syntax/applicativeError.scala
@@ -24,15 +24,18 @@ package syntax
 
 import cats.data.{EitherT, Validated}
 
+import scala.annotation.nowarn
 import scala.reflect.ClassTag
 
 trait ApplicativeErrorSyntax {
   implicit final def catsSyntaxApplicativeErrorId[E](e: E): ApplicativeErrorIdOps[E] =
     new ApplicativeErrorIdOps(e)
 
-  implicit final def catsSyntaxApplicativeError[F[_], E, A](
-    fa: F[A]
-  )(implicit F: ApplicativeError[F, E]): ApplicativeErrorOps[F, E, A] =
+  implicit final def catsSyntaxApplicativeError[F[_], E, A](fa: F[A])(implicit
+    // Although not used directly but helps the compiler to deduce type `E`.
+    @nowarn("cat=unused-params")
+    F: ApplicativeError[F, E]
+  ): ApplicativeErrorOps[F, E, A] =
     new ApplicativeErrorOps[F, E, A](fa)
 }
 
diff --git a/core/src/main/scala/cats/syntax/either.scala b/core/src/main/scala/cats/syntax/either.scala
index 1c4a97e8a4e..220c0ce298e 100644
--- a/core/src/main/scala/cats/syntax/either.scala
+++ b/core/src/main/scala/cats/syntax/either.scala
@@ -24,6 +24,7 @@ package syntax
 
 import cats.data._
 
+import scala.annotation.nowarn
 import scala.reflect.ClassTag
 import scala.util.{Failure, Success, Try}
 import EitherSyntax._
@@ -47,7 +48,11 @@ object EitherSyntax {
    * Uses the [[http://typelevel.org/cats/guidelines.html#partially-applied-type-params Partially Applied Type Params technique]] for ergonomics.
    */
   final private[syntax] class CatchOnlyPartiallyApplied[T](private val dummy: Boolean = true) extends AnyVal {
-    def apply[A](f: => A)(implicit CT: ClassTag[T], NT: NotNull[T]): Either[T, A] =
+    def apply[A](f: => A)(implicit
+      CT: ClassTag[T],
+      @nowarn("cat=unused-params")
+      NT: NotNull[T]
+    ): Either[T, A] =
       try {
         Right(f)
       } catch {
@@ -355,7 +360,7 @@ final class EitherOps[A, B](private val eab: Either[A, B]) extends AnyVal {
   def liftTo[F[_]](implicit F: ApplicativeError[F, _ >: A]): F[B] = F.fromEither(eab)
 }
 
-final class EitherObjectOps(private val either: Either.type) extends AnyVal {
+final class EitherObjectOps(private val either: Either.type) extends AnyVal with EitherObjectOpsBinCompat {
   def left[A, B](a: A): Either[A, B] = Left(a)
 
   def right[A, B](b: B): Either[A, B] = Right(b)
@@ -366,7 +371,8 @@ final class EitherObjectOps(private val either: Either.type) extends AnyVal {
 
   def leftNes[A, B](a: A)(implicit O: Order[A]): EitherNes[A, B] = Left(NonEmptySet.one(a))
 
-  def rightNes[A, B](b: B)(implicit O: Order[B]): EitherNes[A, B] = Right(b)
+  @deprecated("2.8.0", "Use rightNes without Order constraint")
+  protected def rightNes[A, B](b: B)(implicit O: Order[B]): EitherNes[A, B] = Right(b)
 
   def leftNel[A, B](a: A): EitherNel[A, B] = Left(NonEmptyList.one(a))
 
@@ -418,6 +424,10 @@ final class EitherObjectOps(private val either: Either.type) extends AnyVal {
   def unit[A]: Either[A, Unit] = EitherUtil.unit
 }
 
+sealed private[syntax] trait EitherObjectOpsBinCompat extends Any { self: EitherObjectOps =>
+  def rightNes[A, B](b: B): EitherNes[A, B] = Right(b)
+}
+
 final class LeftOps[A, B](private val left: Left[A, B]) extends AnyVal {
 
   /**
diff --git a/tests/shared/src/test/scala/cats/tests/RepresentableStoreSuite.scala b/tests/shared/src/test/scala/cats/tests/RepresentableStoreSuite.scala
index b204a439b8c..65dfaa892b1 100644
--- a/tests/shared/src/test/scala/cats/tests/RepresentableStoreSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/RepresentableStoreSuite.scala
@@ -37,7 +37,7 @@ class RepresentableStoreSuite extends CatsSuite {
 
   {
     implicit val pairComonad: Comonad[RepresentableStore[λ[P => (P, P)], Boolean, *]] =
-      RepresentableStore.catsDataRepresentableStoreComonad[λ[P => (P, P)], Boolean]
+      RepresentableStore.catsDataRepresentableStoreComonadBinCompat[λ[P => (P, P)], Boolean]
     implicit val arbStore: Arbitrary[RepresentableStore[λ[P => (P, P)], Boolean, Int]] =
       catsLawsArbitraryForRepresentableStore[λ[P => (P, P)], Boolean, Int]
     implicit val cogenStore: Cogen[RepresentableStore[λ[P => (P, P)], Boolean, Int]] =