/**
 * Ajax handler for creating new category from Press This.
 *
 * @since 4.2.0
 */
function wp_ajax_press_this_add_category()
{
    include ABSPATH . 'wp-admin/includes/class-wp-press-this.php';
    $wp_press_this = new WP_Press_This();
    $wp_press_this->add_category();
}
<?php

/**
 * Press This Display and Handler.
 *
 * @package WordPress
 * @subpackage Press_This
 */
define('IFRAME_REQUEST', true);
/** WordPress Administration Bootstrap */
require_once dirname(__FILE__) . '/admin.php';
if (!current_user_can('edit_posts') || !current_user_can(get_post_type_object('post')->cap->create_posts)) {
    wp_die('<h1>' . __('Cheatin&#8217; uh?') . '</h1>' . '<p>' . __('Sorry, you are not allowed to create posts as this user.') . '</p>', 403);
}
include ABSPATH . 'wp-admin/includes/class-wp-press-this.php';
$wp_press_this = new WP_Press_This();
$wp_press_this->html();