Try something like this:
/*
* Add custom post type for categories
*
* @return void
*/
function codex_custom_menu_post_init() {
$labels = array(
'name' => 'Menu',
'singular_name' => 'Menu',
'add_new' => 'Add New',
'add_new_item' => 'Add New Menu',
'edit_item' => 'Edit Menu',
'new_item' => 'New Menu',
'all_items' => 'All Menu Items',
'view_item' => 'View Menu',
'search_items' => 'Search Menu',
'not_found' => 'No menu found',
'not_found_in_trash' => 'No menu found in Trash',
'parent_item_colon' => '',
'menu_name' => 'Menu'
);
$args = array(
'labels' => $labels,
'public' => true,
'publicly_queryable' => true,
'show_ui' => true,
'show_in_menu' => true,
'query_var' => true,
'rewrite' => array( 'slug' => 'menu' ),
'capability_type' => 'post',
'has_archive' => true,
'hierarchical' => false,
'menu_position' => 5,
'menu_icon' => "dashicons-editor-justify",
'supports' => array( 'title', 'editor', 'thumbnail', 'custom-fields'/*, 'excerpt'*/),
'taxonomies' => array( 'post_tag', 'category' )
);
register_post_type( 'menu', $args );
}
add_action( 'init', 'codex_custom_menu_post_init' );