Wordpress Category & Sub Category Help Needed

I would like to have a menu consisting of categories and, when hovered over shows shows sub categories. Because of the nature of my theme, I am not making use of the sidebar.php , instead I have pasted this in my header.php:

<div id="sidebar">
<?php if ( function_exists('dynamic_sidebar') && dynamic_sidebar(1) ) ?>
</div>
​

Ive added a custom php widget to my "sidebar". In that widget is the following code:

<?php wp_list_categories('title_li='); ?>
​

This is as far as I have got, but need help getting it to hover and display the correct sub category.

 

If you use the sidebar, will the sub-categories display correctly?