return new WrappedSet(key, (Set<V>) collection);
      } else {
        return new WrappedCollection(key, collection, null);
      }
    }

    // can't use Serialization writeMultimap and populateMultimap methods since
    // there's no way to generate the empty backing map.

    /**
     * @serialData the factory and the backing map
     */
    @GwtIncompatible
    @J2ktIncompatible

  @GwtIncompatible
  @J2ktIncompatible
    private void writeObject(ObjectOutputStream stream) throws IOException {
    stream.defaultWriteObject();
    stream.writeObject(valueComparator());
    Serialization.writeMultimap(this, stream);
  }

  private @Nullable Comparator<? super V> valueComparator() {
    return emptySet instanceof ImmutableSortedSet
        ? ((ImmutableSortedSet<V>) emptySet).comparator()
        : null;

  @GwtIncompatible
  @J2ktIncompatible
    private void writeObject(ObjectOutputStream stream) throws IOException {
    stream.defaultWriteObject();
    stream.writeObject(valueComparator());
    Serialization.writeMultimap(this, stream);
  }

  private @Nullable Comparator<? super V> valueComparator() {
    return emptySet instanceof ImmutableSortedSet
        ? ((ImmutableSortedSet<V>) emptySet).comparator()
        : null;