WordPress and woocommerce: register product custom taxonomy

function my_custom_taxonomy_item() {

$labels = array(
'name' => 'composers',
'singular_name' => 'Composer',
'menu_name' => 'Composers',
'all_items' => 'All Composers',
'parent_item' => 'Parent Composer',
'parent_item_colon' => 'Parent Composer:',
'new_item_name' => 'New Composer Name',
'add_new_item' => 'Add New Composer',
'edit_item' => 'Edit Composer',
'update_item' => 'Update Composer',
'separate_items_with_commas' => 'Separate Composers with commas',
'search_items' => 'Search Composers',
'add_or_remove_items' => 'Add or remove Composers',
'choose_from_most_used' => 'Choose from the most used Composers',
);
$args = array(
'labels' => $labels,
'hierarchical' => true,
'public' => true,
'show_ui' => true,
'show_admin_column' => true,
'show_in_nav_menus' => true,
'show_tagcloud' => true,
);

register_taxonomy( 'composers', 'product', $args );

}

add_action( 'init', 'my_custom_taxonomy_item', 0 );

Thanks to: https://gist.github.com/themepaint/b3755d6c8d6070dac40643c6ce8210e9, https://codex.wordpress.org/Function_Reference/register_taxonomy