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