Custom categories not showing up on Page Edit screen :(

I added this code to my functions.php file to add custom categories to the native WP Pages. But they are not showing up when I go to edit the page. I expected that on the right sidebar it would be one of the widgets but it’s not there. Am I missing anything here?

function pagecategory_taxonomy()
{

    $labels = array(
        'name'                       => _x('Page Categories', 'Taxonomy General Name', 'text_domain'),
        'singular_name'              => _x('Page Category', 'Taxonomy Singular Name', 'text_domain'),
        'menu_name'                  => __('Categories', 'text_domain'),
        'all_items'                  => __('All Categories', 'text_domain'),
        'parent_item'                => __('Parent Category', 'text_domain'),
        'parent_item_colon'          => __('Parent Category:', 'text_domain'),
        'new_item_name'              => __('New Category Name', 'text_domain'),
        'add_new_item'               => __('Add New Category', 'text_domain'),
        'edit_item'                  => __('Edit Category', 'text_domain'),
        'update_item'                => __('Update Category', 'text_domain'),
        'view_item'                  => __('View Item', 'text_domain'),
        'separate_items_with_commas' => __('Separate page categories with commas', 'text_domain'),
        'add_or_remove_items'        => __('Add or remove page categories', 'text_domain'),
        'choose_from_most_used'      => __('Choose from the most used page categories', 'text_domain'),
        'popular_items'              => __('Popular Items', 'text_domain'),
        'search_items'               => __('Search page categories', 'text_domain'),
        'not_found'                  => __('Not Found', 'text_domain'),
        'no_terms'                   => __('No items', 'text_domain'),
        'items_list'                 => __('Items list', 'text_domain'),
        'items_list_navigation'      => __('Items list navigation', 'text_domain'),
    );
    $args = array(
        'labels'                     => $labels,
        'hierarchical'               => true,
        'public'                     => true,
        'show_ui'                    => true,
        'show_admin_column'          => true,
        'show_in_nav_menus'          => true,
        'show_tagcloud'              => false,
    );
    register_taxonomy('page_category', array('page'), $args);
}
add_action('init', 'pagecategory_taxonomy', 0);