Сам код:
<?php
include $_SERVER['DOCUMENT_ROOT'].'/incs/system.php';
$array = array();
$empty = NULL;
$sql = $db->query("SELECT c.name, c.id, COUNT(p.cat_id) AS cnt FROM `categories` AS c LEFT JOIN projects AS p ON p.cat_id = c.id GROUP BY c.name");
while($row = $sql->fetch_assoc()) {...