使用php更改sql变量的问题

Question

我有多个产品类别，因此根据我点击的页面，我希望能够将WHERE pc.item_category_id = 3更改为pc.item_category_id = $cat_value。

test.php的

<div id="get_product" class="form-row">
    // <?php $cat_value = 3; ?> does not work, error in sql
</div>

action.php的

if(isset($_POST["getProduct"])){
    $product_query = "SELECT * FROM product_items as pi 
                    INNER JOIN product_category as pc ON pi.item_category = pc.item_category
                    WHERE pc.item_category = 3 // need to be able to change that to a variable like $cat_value
                    ORDER BY pi.product_item_id LIMIT $start, $limit";
    $result = $conn->query($product_query);
    etc...
    //WHERE pc.item_category = 3 to WHERE pc.item_category = $cat_value does not work
}

test.js

function product(){
    $.ajax({
        url :   "action.php",
        method: "POST",
        data    :   {getProduct:1},
        success :   function(data){
            $("#get_product").html(data);
        }
    })
}