Substitute this for the appropriate capitalized terms:
$category->slug;
$category->description;
$category->parent;
Look at the database schema for Terms (or categories in older WordPress) – basically any field can be called by the field name you see in the table.
$category->parent returns the ID of the parent category, so if you need something else you’ll need to use the method calls that take cat_ID as an argument.
(http://www.estsn.com/ – it’s WordPress)