recursive query in a product catalog tree?

[peter michaux]

I have a catalog like the following

CREATE TABLE category (
category_id INTEGER(10) UNSIGNED NOT NULL auto_increment,
parent_category_id int(10) unsigned NOT NULL default '0',
PRIMARY KEY (category_id)
) ENGINE=innoDB;

CREATE TABLE product (
product_id INTEGER(10) UNSIGNED NOT NULL auto_increment,
name varchar(10) NOT NULL default '',
PRIMARY KEY (product_id)
) ENGINE=innoDB;

# a product can be in multiple categories
CREATE TABLE category_product (
category_id INTEGER(10) UNSIGNED NOT NULL default '0',
product_id INTEGER(10) UNSIGNED NOT NULL default '0',
PRIMARY KEY (category_id, product_id)
) ENGINE=innoDB;

With only one query I would like to find all the categories that a product is in up the tree to a top level category with parent_category_id==0. To me this seems like a recursive search up the tree. The only way I can think to do it is to get the categories that a product is in and then for each one follow the tree up step buy step. But this takes many queries and a loop in PHP.

Is there a single step query that will do this?

Thanks,
Peter