从数据库显示类别显示空结果

I got 3 tables, products, categories, and prod_cat the id of products and the id of categories are related to the prod_cat id_cat and id_prod.

i want to display the products of a certain category to show it, so i wrote this code:

$cat=$_POST['cat'];
$sql = mysql_query("SELECT products.id, products.product_name, products_cat.prod_id FROM products
INNER JOIN products_cat ON products.id=products_cat.prod_id ORDER BY products.id");
$catCount = mysql_num_rows($sql); // count the output amount
    while($row = mysql_fetch_array($sql)){ 
             $id = $row["id"];
             $product_name = $row["product_name"];
             $price = $row["price"];
             $date_added = strftime("%b %d, %Y", strtotime($row["date_added"]));
             $prod_list .= "category ID: $id - <strong>$product_name</strong> <br />";

but when i display the prod_list variable on the page it is empty, what did i do wrong ???

btw, i want to display like that: www.mydomain.com/show.php?cat=x