Okay, solved it myself. I used a VERY primitive method.
The code, in case anyone needs to do anything similar in the future.
<?php
$category = get_the_category();
$parent = get_cat_name($category[0]->category_parent);
if (!empty($parent))
{
echo '<a href="', bloginfo('url'), '/', $parent, '/">', $parent, '</a>';
}
else
{
echo the_category(', ');
}
?>