Get Category of Parent within the {parents} tag

I have two channels - Parent and Child

Parent: Batteries. This Channel has categories. I create an entry in Battery (ex: AAA) and add it to the “Disposable” category. I then relate this entry to it’s brand: Panasonic.

So the end result is it is AAA, Disposable and is Panasonic

Child: Brand This is just a channel where I create all the brands

What I am trying to do: Create a page where I list all batteries and sort them by brand and show the type - disposable or rechargeable (which are categories).

This is what I have so far. Showing the categories is where I’m having trouble and help will be appreciated.

<div class="row">
 <div class="col-sm-12">
  {exp:channel:entries channel="brands" dynamic="no" orderby="title" sort="asc"}
   <div class="row clearfix m-b-50">
    <h2>{title}</h2>
    {parents field="brand" channel="batteries" orderby="title" sort="asc" limit="6"}
        <div class="col-md-2">
         Type: {categories}{category_name}{/categories}

         <a href="/{segment_1}/{parents:url_title}">{parents:title}</a>
        </div>
    {/parents}
   </div>
  {/exp:channel:entries}
 </div>
</div>