I'm sorry, slight error in my post
You will not be able to get unique categorys if you select the id field in the table as well. If you don't need the id field, I would recommend the following
mysql_query("SELECT DISTINCT category FROM publications_hilites WHERE category='$this_category'");
If you are just looking for the id of one of the items in a particular category you could just add a LIMIT 0, 1 to the end of the query.
It's a hard question to answer exactly since I am not sure what you are trying to accomplish