Thanks for that, but it's not quite working the way I want...
So inside of the main loop (index.php) I have it targeting the specific category
<?php query_posts('cat=14&showposts=3'); ?>
<?php $posts = get_posts('category=14&numberposts=3&offset=0');
foreach ($posts as $post) : start_wp(); ?>
Then I have a ul with the li's inside of that. I want to give each li in the loop a class of all the sub-categories that is assigned to it. For example
<ul>
<li class="Video Project"></li>
<li class="Project About"></li>
</ul>
When I was using your code that you provided earlier I was getting some sub-categories names as Blog-Video. (Blog is the main Category)
So in the above example I want to only have the sub-categories of category 14 (bold above) to show up.