Custom taxonomies

Hi, I tried to create custom taxonomies for woocommerce products, but it doesn’t work. Better, I created them and I see them when I create a new product, but in front-end, when I go to, the browsaer shows the related products as wordpress posts and not as woocommerce posts.
The code is this:

add_action( 'init', 'tassonomia_editore', 0 );
function tassonomia_editore()  {
$labels = array(
    'name'                       => _x( 'editore', 'taxonomy general name' ),
    'menu_name'                  => __( 'editore' ),
    'all_items'                  => __( 'Tutti gli Editori' ),
    'parent_item'                => __( 'editore Principale' ),
    'parent_item_colon'          => __( 'editore Principale:' ),
    'new_item_name'              => __( 'Nuovo editore' ),
    'add_new_item'               => __( 'Aggiungi un nuovo editore' ),
    'edit_item'                  => __( 'Modifica editore' ),
    'update_item'                => __( 'Aggiorna editore' ),
    'separate_items_with_commas' => __( 'Separa i termini con le virgole' ),
    'search_items'               => __( 'Cerca' ),
    'add_or_remove_items'        => __( 'Aggiungi o rimuovi editore' ),
    'choose_from_most_used'      => __( 'Scegli tra gli Editori più utilizzati' ),
$args = array(
    'labels'                     => $labels,
    'hierarchical'               => true,
    'show_ui'                    => true,
    'show_admin_column'          => true,
    'show_in_nav_menus'          => true,
    'show_tagcloud'              => true,
        'query_var'                                      => true,
        'update_count_callback' => '_update_post_term_count',
register_taxonomy( 'editore', 'product', $args );

and I think it is right.

In worst cases, this code in child theme functions.php file makes the terrific white page for all pages of the site, also for the admin back-end.

Do you have an idea? Where is the problem in your opinion? Is it a theme problem or not?
Bye and have a good Easter!

Are you sure that you need custom taxonomy instead of much more flexible Product Attributes?

I am not very familiar with WooCommerce. This theme has basic support for it but it is not a complete ecommerce solution, therefore there might be some issues.