Doctrine fetching filtered associated objects with findAll

Question

I' searched all over the Internet but I've not found a definite answer to this question. I have the following entities:

/**
* @ORM\Entity
* @ORM\Table(name="category")
*/
class Category
{
    /*
     * ...
     */

    /**
     * @ORM\OneToMany(targetEntity="Product", mappedBy="category")
     */
    protected $products;

    public function __construct()
    {
        $this->products = new ArrayCollection();
    }

    /**
     * Add product
     *
     * @param \AppBundle\Entity\Product $product
     *
     * @return Category
     */
    public function addProduct(\AppBundle\Entity\Product $product)
    {
        $this->products[] = $product;

        return $this;
    }

    /**
     * Remove product
     *
     * @param \AppBundle\Entity\Product $product
     */
    public function removeProduct(\AppBundle\Entity\Product $product)
    {
        $this->products->removeElement($product);
    }

    /**
     * Get products
     *
     * @return \Doctrine\Common\Collections\Collection
     */
    public function getProducts()
    {
        return $this->products;
    }

}

/**
 * @ORM\Entity
 * @ORM\Table(name="product")
 */
class Product
{
    /*
     * ...
     */

    /**
     * @ORM\ManyToOne(targetEntity="Category", inversedBy="products")
     * @ORM\JoinColumn(name="category_id", referencedColumnName="id")
     */
    protected $category;

    /**
     * @ORM\Column(type="boolean")
     */
    protected $active;

    /**
     * Set category
     *
     * @param \AppBundle\Entity\Category $category
     *
     * @return Product
     */
    public function setCategory(\AppBundle\Entity\Category $category = null)
    {
        $this->category = $category;

        return $this;
    }

    /**
     * Get category
     *
     * @return \AppBundle\Entity\Category
     */
    public function getCategory()
    {
        return $this->category;
    }

    /**
     * Set active
     *
     * @param boolean $active
     *
     * @return Product
     */
    public function setActive($active)
    {
        $this->active= $active;

        return $this;
    }

    /**
     * Get active
     *
     * @return boolean
     */
    public function getActive()
    {
        return $this->active;
    }
}

I only want to do this:

$em = $this->getDoctrine()->getManager();
$categories = $em->getRepository('AppBundle\Entity\Category')->findAll();        
$json = $serializer->serialize($categories, 'json');

and in the json result I want to make sure that all categories have their associated products filtered by status=true.In other words I want to get the results in the front end as an array of category objects with each category having an array of products that are active only.

I know it can be done trivially in Django.

Can it be done in doctrine?If yes how. Strait answers please.

SOLUTION I'VE USED

$qb = $em->createQueryBuilder()
      ->select('c')
      ->from('AppBundle:Category','c')
      ->leftJoin('c.products','p','WITH','p.status = :status')
      ->addSelect('p')
      ->setParameter('status', true);