<? echo $form->field($model1, 'operation')->hiddenInput(['value' => 'hidden value']); ?>

$provider_top = new ActiveDataProvider([
            'query' => Object::find()->where(['status' => 1])->orderBy(['visits'=>SORT_DESC]),
            'pagination' => [
                'pageParam' => 'page-top', # <-------------
                'pageSize' => 6,
            ],
        ]);
$provider_new = new ActiveDataProvider([
            'query' => Object::find()->where(['status' => 1])->orderBy(['added_on'=>SORT_DESC]),
            'pagination' => [
                'pageParam' => 'page-new', # <-------------
                'pageSize' => 6,
            ],
        ]);

$categories = app\models\Category::findAll();
$data = yii\helpers\ArrayHelper::map($categories, 'id', 'name');
$form->field($model, 'parent_id')->dropDownList($data);

....
'select'=>'js:function( event, ui ) {
// вот тут лежит ID
    ui.item.id    

}',
....