How to display array sent back from Ajax Request. Using Yii2

I have sent of an ajax request, it then will query the database and send back what I want. However I am stuck on actually displaying this when it is returned to my page.

$.ajax({
    url: '<?php echo \Yii::$app->getUrlManager()->createUrl('cases/ajax') ?>',
    type: 'POST',
    data: { firstcategory: firstcategory },
    success: function(data) {
        for (var key in data) {
            var value = data[key];
            alert(value);
            document.write(value);
        }   
    }
});

As you can see, I am trying to display the value but it is coming back with an array.

This is what is being sent back from ajax request:

Array
(
[0] => app\models\Subcategory Object
    (
        [_attributes:yii\db\BaseActiveRecord:private] => Array
            (
                [subcategory_id] => 1
                [name] => ADJUDICATION ON BEHALF OF OR AGAINST AN INSOLVENT PARTY
                [parent_id] => 2
            )

        [_oldAttributes:yii\db\BaseActiveRecord:private] => Array
            (
                [subcategory_id] => 1
                [name] => ADJUDICATION ON BEHALF OF OR AGAINST AN INSOLVENT PARTY
                [parent_id] => 2
            )

        [_related:yii\db\BaseActiveRecord:private] => Array
            (
            )

        [_errors:yii\base\Model:private] => 
        [_validators:yii\base\Model:private] => 
        [_scenario:yii\base\Model:private] => default
        [_events:yii\base\Component:private] => Array
            (
            )

        [_behaviors:yii\base\Component:private] => Array
            (
            )

    )

[1] => app\models\Subcategory Object
    (
        [_attributes:yii\db\BaseActiveRecord:private] => Array
            (
                [subcategory_id] => 2
                [name] => THE EXISTENCE OF A CONTRACT
                [parent_id] => 3
            )

        [_oldAttributes:yii\db\BaseActiveRecord:private] => Array
            (
                [subcategory_id] => 2
                [name] => THE EXISTENCE OF A CONTRACT
                [parent_id] => 3
            )

        [_related:yii\db\BaseActiveRecord:private] => Array
            (
            )

        [_errors:yii\base\Model:private] => 
        [_validators:yii\base\Model:private] => 
        [_scenario:yii\base\Model:private] => default
        [_events:yii\base\Component:private] => Array
            (
            )

        [_behaviors:yii\base\Component:private] => Array
            (
            )

    )

[2] => app\models\Subcategory Object
    (
        [_attributes:yii\db\BaseActiveRecord:private] => Array
            (
                [subcategory_id] => 3
                [name] => THE MEANING OF CONSTRUCTION CONTRACT
                [parent_id] => 3
            )

        [_oldAttributes:yii\db\BaseActiveRecord:private] => Array
            (
                [subcategory_id] => 3
                [name] => THE MEANING OF CONSTRUCTION CONTRACT
                [parent_id] => 3
            )

        [_related:yii\db\BaseActiveRecord:private] => Array
            (
            )

        [_errors:yii\base\Model:private] => 
        [_validators:yii\base\Model:private] => 
        [_scenario:yii\base\Model:private] => default
        [_events:yii\base\Component:private] => Array
            (
            )

        [_behaviors:yii\base\Component:private] => Array
            (
            )

    )
  )

Okay, now I want to display the data in just this section:

[subcategory_id] => 1
[name] => ADJUDICATION ON BEHALF OF OR AGAINST AN INSOLVENT PARTY
[parent_id] => 2

How do i achieve this in javascript when i receive the data back in the variable "data"?

Thanks for any help you can give me

Edit:

This is my controller:

public function actionAjax() {
    if(isset($_POST['firstcategory'])) {
        $firstcategory = $_POST['firstcategory'];
        $subcategory = Subcategory::find()->all();
    } else {
        $firstcategory = "Ajax failed";
    }

    print_r($subcategory);
    exit;

    return \yii\helpers\Json::encode($subcategory);
}

Second edit:

I receive this json

[
    {
        "subcategory_id": "1",
        "name": "ADJUDICATION ON BEHALF OF OR AGAINST AN INSOLVENT PARTY",
        "parent_id": "2"
    },
    {
        "subcategory_id": "2",
        "name": "THE EXISTENCE OF A CONTRACT",
        "parent_id": "3"
    },
    {
        "subcategory_id": "3",
        "name": "THE MEANING OF CONSTRUCTION CONTRACT",
        "parent_id": "3"
    },
    {
        "subcategory_id": "4",
        "name": "THE MEANING OF CONSTRUCTION OPERATIONS",
        "parent_id": "3"
    },
    {
        "subcategory_id": "5",
        "name": "EXCLUDED CONSTRUCTION OPERATIONS",
        "parent_id": "3"
    },
    {
        "subcategory_id": "6",
        "name": "EXCLUDED AGREEMENTS",
        "parent_id": "3"
    }
]

Now in my view I am trying to parse it but I'm unsure

success: function(data) {
    obj = JSON.parse(data);
    document.write(obj.subcategory_id);
}

This isn't working?