update my JOIN table - php

Question

I have built a system where I can create a category and a document. the categories live in the cat_list table and the documents live in the doc_list table. there is a column in the doc_list table called cat_no which takes an array or the categories that belong to that doc.
newfile.php
<?php
require_once '../../db_con.php';
try{
// Selecting entire row from cat_list table
$results = $dbh->query("SELECT * FROM cat_list");
}catch(Exception $e) {
echo $e->getMessage();
die();
}
$cat = $results->fetchAll(PDO::FETCH_ASSOC);
?>
<form action="actions/newDocAdd.php" method="post" id="rtf" name="">
<input type="text" name="doc_title" id="doc_title" required="required" placeholder="Document Title"/><br />
<?php
foreach($cat as $cat){
echo
'<input type="checkbox" value="" name=""> ' .$cat["cat_title"]. '</a><br>';
}
?>
<br><br>
<textarea name="doc_content" id="doc_content" placeholder="Document Content" style="display: none;"></textarea>
<iframe name="editor" id="editor" style="width:100%; height: 600px;"></iframe>
<br><br>
<input onclick="formsubmit()" type="submit" value="Create Document" name="submit"/>
</form>
I have cut alot out of the form because there is alot of JS because it is a WYSIWYG creator hence the iframe. But the key area is where I lsit out categories above as checkboxes, I need to allow for that to then post a number (or array of numbers if more than one is clicked) into the col_no column in the doc)list table.
Here is the script which posts the data:
<?
session_start();
session_regenerate_id();
if(!isset($_SESSION['user'])){
header("Location: ../index.php");
exit;
}
if(isset($_POST["submit"])){
include_once'../../config.php';
try {
$dbh = new PDO("mysql:host=$hostname;dbname=dashboardr",$username,$password);
$dbh->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION); // <== add this line
$sql = "INSERT INTO doc_list (doc_title, doc_content, doc_created, user_id) VALUES ('".$_POST["doc_title"]."','".$_POST["doc_content"]."', NOW(), '".$_SESSION['user']."''".$_POST['cat_no']."' )";
print_r($_POST);
if ($dbh->query($sql)) {
header ('Location: ../docList.php?success=1');
}
else{
}
$dbh = null;
}
catch(PDOException $e)
{
echo $e->getMessage();
}
}
?>
UPDATE
<?php
foreach($cat as $cat){
echo
'<input type="checkbox" value="$cat["cat_id"]" name="cat_no"> ' .$cat["cat_title"]. '</a><br>';
}
?>
So I can get it to post in a value of "0" but I need it to be an array of the ID's of which I am posting, what is it I am doing wrong here?