diff --git a/compiler/src/dotty/tools/dotc/core/Types.scala b/compiler/src/dotty/tools/dotc/core/Types.scala
index 955a5a11c6f2..5be397a3e5e4 100644
--- a/compiler/src/dotty/tools/dotc/core/Types.scala
+++ b/compiler/src/dotty/tools/dotc/core/Types.scala
@@ -2219,7 +2219,7 @@ object Types {
 
     def derivedAndType(tp1: Type, tp2: Type)(implicit ctx: Context): Type =
       if ((tp1 eq this.tp1) && (tp2 eq this.tp2)) this
-      else AndType.make(tp1, tp2)
+      else AndType.make(tp1, tp2, checkValid = true)
 
     def derived_& (tp1: Type, tp2: Type)(implicit ctx: Context): Type =
       if ((tp1 eq this.tp1) && (tp2 eq this.tp2)) this
@@ -2234,21 +2234,26 @@ object Types {
   final class CachedAndType(tp1: Type, tp2: Type) extends AndType(tp1, tp2)
 
   object AndType {
-    def apply(tp1: Type, tp2: Type)(implicit ctx: Context) = {
+    def apply(tp1: Type, tp2: Type)(implicit ctx: Context): AndType = {
       assert(tp1.isValueType && tp2.isValueType, i"$tp1 & $tp2 / " + s"$tp1 & $tp2")
       unchecked(tp1, tp2)
     }
-    def unchecked(tp1: Type, tp2: Type)(implicit ctx: Context) = {
+
+    def unchecked(tp1: Type, tp2: Type)(implicit ctx: Context): AndType = {
       assertUnerased()
       unique(new CachedAndType(tp1, tp2))
     }
-    def make(tp1: Type, tp2: Type)(implicit ctx: Context): Type =
+
+    /** Make an AndType using `op` unless clearly unnecessary (i.e. without
+     *  going through `&`).
+     */
+    def make(tp1: Type, tp2: Type, checkValid: Boolean = false)(implicit ctx: Context): Type =
       if ((tp1 eq tp2) || (tp2 eq defn.AnyType))
         tp1
       else if (tp1 eq defn.AnyType)
         tp2
       else
-        apply(tp1, tp2)
+        if (checkValid) apply(tp1, tp2) else unchecked(tp1, tp2)
   }
 
   abstract case class OrType(tp1: Type, tp2: Type) extends CachedGroundType with AndOrType {
@@ -2994,7 +2999,7 @@ object Types {
   // ----- Skolem types -----------------------------------------------
 
   /** A skolem type reference with underlying type `binder`. */
-  abstract case class SkolemType(info: Type) extends UncachedProxyType with ValueType with SingletonType {
+  case class SkolemType(info: Type) extends UncachedProxyType with ValueType with SingletonType {
     override def underlying(implicit ctx: Context) = info
     def derivedSkolemType(info: Type)(implicit ctx: Context) =
       if (info eq this.info) this else SkolemType(info)
@@ -3010,13 +3015,6 @@ object Types {
     override def toString = s"Skolem($hashCode)"
   }
 
-  final class CachedSkolemType(info: Type) extends SkolemType(info)
-
-  object SkolemType {
-    def apply(info: Type)(implicit ctx: Context) =
-      unique(new CachedSkolemType(info))
-  }
-
   // ------------ Type variables ----------------------------------------
 
   /** In a TypeApply tree, a TypeVar is created for each argument type to be inferred.
diff --git a/tests/neg/i2232.scala b/tests/neg/i2232.scala
new file mode 100644
index 000000000000..e0f83683d42a
--- /dev/null
+++ b/tests/neg/i2232.scala
@@ -0,0 +1,37 @@
+object Cats {
+  trait Trivial[A]
+  implicit def trivial[A]: Trivial[A] = new Trivial[A] { }
+
+  type Obj[C[_[_[_], _[_, _]]]] =
+    [A]    => C[({type l[c0[_], c1[_, _]] = c0[A]   })#l]
+  type Cat[C[_[_[_], _[_, _]]]] =
+    [A, B] => C[({type l[c0[_], c1[_, _]] = c1[A, B]})#l]
+
+  trait Category[C[_[_[_], _[_, _]]]] {
+    type ->  = Cats.Cat[C]
+    type Obj = Cats.Obj[C]
+
+    def id[A: Obj]: A -> A
+    def andThen[A, B, C](ab: A -> B, bc: B -> C): A -> C
+  }
+
+  object Category {
+    type ByF[F[_, _]] = Category[_] { type -> = F }
+  }
+
+  type Scal[f[_[_], _[_, _]]] = f[Trivial, Function1]
+
+  implicit val scal: Category[Scal] = new Category[Scal] {
+    def id[A: Obj]: A -> A = a => a
+    def andThen[A, B, C](ab: A -> B, bc: B -> C): A -> C = ab.andThen(bc)
+  }
+
+  implicit class CategoryOps[F[_, _], A, B](ab: F[A, B]) {
+    def >>>[C](bc: F[B, C])(implicit F: Category.ByF[F]): F[A, C] =
+      F.andThen(ab, bc)
+  }
+
+  val f: Int => Int = _ + 1
+  val g: Int => String = _.toString
+  f >>> g   // error: no implicit arg found
+}