I, too, am trying to list each category with its own class. I would like the output to look like something like this in my sidebar:
a href="http://mydomain.com/?cat=1" cat=1/a
a href="http://mydomain.com/?cat=2" cat=2 /a
a href="http://mydomain.com/?cat=3" cat=3 /a
This way I can create a style for each category and color code them.
I have already figured out how to call the different class names by using the php the_category_unlinked('') tag and using the category slug as the class name.
All I need to do is figure out how to get the class= into the line.