Yii2 dropdown multiple selected values

all your code is ok just need echo your $form->...

echo $form->field($model, 'categories[]')            
     ->dropDownList($model->CategoryDropdown,
     [
      'multiple'=>'multiple',
      'class'=>'chosen-select input-md required',              
     ]             
    )->label("Add Categories"); 

or use <?= ?> in view!

Here is solution:

Form

 <?= 
  $form->field($model, 'categories')            
         ->dropDownList($model->CategoryDropdown,
         [
          'class'=>'chosen-select input-md required',
          'multiple'=>'multiple'              
         ]             
        )->label("Add Categories");
 ?>

Controller:

 public function actionCreate(){
 ...
     $model->categories = implode(",",$_POST['Company']['categories']);
    ...
    return $this->render('create', [
            'model' => $model,           
        ]);
 }

public function actionUpdate($id)
{
    $model = $this->findModel($id); 
    $model->categories = explode(',', $model->categories);        
    ...
    if($model->load(Yii::$app->request->post()))
    {
         $model->categories = implode(",",$_POST['Company']['categories']);    
         ...
         $model->save()
    }
    return $this->render('update', [
                'model' => $model,                    
            ]); 
  }