What the error of update function? - php

Question

I development admin control panel in my system when i update some thing in category the data not updated. what the error of my code? for more help you can download my files from here http://www.mediafire.com/download/m9psmr55pib5555/update_category.rar
<form action="categories.php" method="post">
<label>Edit category</label>
<?php
/*start of select data */
if(isset($_GET['edit_cat'])){
$cat_id = $_GET['edit_cat'];
$update_cat ="SELECT * FROM categories WHERE cat_id= $cat_id";
$run_cat_id = mysqli_query($connect , $update_cat);
while($row =mysqli_fetch_assoc($run_cat_id)){
$cat_id = $row['cat_id'];
$cat_title = $row['cat_name'];
?>
<div class="form-group">
<!--to pick the value -->
<input value="<?php if(isset($cat_title)){echo $cat_title;} ?>" type="text" class="form-control" name="cat_name">
</div>
<?php }}?>
<?php
if(isset($_POST['update'])){
$cat_update = $_POST['cat_name'];
$query ="UPDATE categories SET cat_name ='{$cat_update}' WHERE cat_id ={$cat_id}";
$update_query= mysqli_query($connect , $query);
<?php
ob_start();
include("includes/header.php");
include("includes/db.php");
?>
<div id="page-wrapper">
<div class="container-fluid">
<?php
if(isset($_GET['edit_cat'])){
$cat_id = $_GET['edit_cat'];
include ("includes/update_category.php");
}
?>
</div>
<!-- end of category form -->
</div>
<!--
===========================================================================================================
-->
<!-- start of table to show categories-->
<div class="col-lg-6">
<div class="btn btn-success"><h3>categories</h3></div>
<div class="table-responsive" >
<table class="table table-bordered table-hover">
<thead>
<tr>
<th width="10px">Id</th>
<th width="400px">category title</th>
</tr>
</thead>
<tbody>
<?php
/*Select from DB to show categories in table*/
$i=1;
$query = "SELECT *FROM categories";
$run_cat = mysqli_query($connect , $query);
while($row = mysqli_fetch_assoc($run_cat)){
$cat_id = $row['cat_id'];
$cat_name =$row ['cat_name'];
?>
<tr>
<td><?php echo $i++;?></td>
<td><?php echo $cat_name; ?></td>
<td><div class='btn btn-warning' name="edit_cat"><i class='fa fa-pencil-square-o fa-2'></i> Edit</div></td>
</tr>
<?php } ?>
</tbody>
</table>
</div>
<!-- end of table to show categories-->
<!-- =============================================================================
-->
</div>
</div>
</div>
</body>
</html>
if(!$update_query){
die("QUERY FAILED".mysqli_error($connect));
}
}
?>
<div class="form-group">
<input type="submit" name="update" value="submit" class="btn btn-success"/>
</div>
</form>