在产品页面上显示属于类别

I try to show what categories the product is included in the product page with a fillter so I only show the product in a certain category or its subcategories.

I have a category (id 10) I put all the campaigns in subcategories At the product level, I would then see if the product is in category 10 or its sub-categories with a clickable link to the category.

Here's is what i got so far. This code bellow gives med all categories that the product is in

<?php
    $currentCatIds = $_product->getCategoryIds();
    $categoryCollection = Mage::getResourceModel('catalog/category_collection')
    ->addAttributeToSelect('name')
    ->addAttributeToSelect('url')
    ->addFieldToFilter('level', array('eq' => 4))
    ->addAttributeToFilter('entity_id', $currentCatIds)
    ->addIsActiveFilter();
?>

And here is my output

<?php foreach($categoryCollection as $cat):?>
    <a href="<?php echo $cat->getUrl(); ?>" title="<?php echo $cat->getName();  ?>"><?php echo $cat->getName();?></a></br>
<?php endforeach; ?>