How to add categories to page editor?

by

You’ll need to register the category taxonomy for the page post_type with register_taxonomy_for_object_type.

This does the trick:

<?php
add_action( 'init', 'wpse34528_add_page_cats' );
function wpse34528_add_page_cats()
{
    register_taxonomy_for_object_type( 'category', 'page' );
}