How to add categories to page editor?

I’m trying to add the categories selector to the “page” editor workspace. The code below does the trick, however, none of the values are saved with the page.

Any help much appreciated!

add_action('admin_menu', 'my_post_categories_meta_box');
function my_post_categories_meta_box() {
    add_meta_box('categorydiv', __('Categories'),      
   'post_categories_meta_box', 'page', 'side', 'core');
}