Foreign key constraint is incorrectly formed (MySQL)
Without seeing your categories table, your only problem is that the referenced columns like inart_ps_category_id need an index, which you can achieve by using KEY(inart_ps_category_id):
CREATE TABLE IF NOT EXISTS `inart_ps_categories` (
  `id` int(11) UNSIGNED NOT NULL AUTO_INCREMENT,
  `inart_ps_category_id` int(11) UNSIGNED NOT NULL,
  `parent_id` int(11) UNSIGNED DEFAULT NULL,
  `name` varchar(255) DEFAULT NULL,
  `path` varchar(255) DEFAULT NULL,
  `num_children` int(11) DEFAULT '0',
  `flag` tinyint(1) NOT NULL,
  PRIMARY KEY (`id`),
  KEY(`inart_ps_category_id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE utf8_general_ci;

CREATE TABLE IF NOT EXISTS `inart_ps_category_associations` (
  `id` int(11) UNSIGNED NOT NULL AUTO_INCREMENT,
  `inart_ps_category_id` int(11) UNSIGNED NOT NULL,
  `categoryid` int(11) NOT NULL,
  PRIMARY KEY (`id`),
    FOREIGN KEY (categoryid) REFERENCES `categories` (categoryid) ON DELETE CASCADE,
    FOREIGN KEY (inart_ps_category_id) REFERENCES `inart_ps_categories` (inart_ps_category_id) ON DELETE CASCADE
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE utf8_general_ci;