Александр

$params = [
    "id" => $array['category_id'],
    "cat_name" => $array['category_name'],
    "cat_url" => $array['category_url'],
    "image_url" => $array['image_url'],
    "parent_cat" => $array['parent_cat'],
];

$a = [];
foreach ($params as $k => $v) {
    $a[] = "`$k` = :$k";
}

if (count($a)) {
    $s = implode(", ", $a);
    $sql = "UPDATE {$this->table} SET $s WHERE `id` = :id";
}