How to get the nicename of a parent category?

I am creating a link to help users navigate backwards in a category template.
What works:

<a href="<?php
//this link works perfectly
echo get_category_link ( $category->category_parent );?>">
Back to <?php
//this displays the parent category id number
echo the_category($category->category_parent);?></a>

The above returns:
Back to 10
With the link in tact, and the 10 being the current category’s parent cat ID.

How do I get it to simply list he category nice name based on the ID above?

Thanks!