Use another custom post type as parent

Hello,
I have two custom post types: Category and Product

What I want to do is select Category pages as the parent for Product pages. Is this possible? The code that I’m using to register these is the following.

/* Category Post Type */
    add_action('init', 'Category_post_type_init');
    function Category_post_type_init() {
      $labels = array(
        'name' => _x('Category', 'post type general name'),
        'parent_item_colon' => __('Category'),
            'parent' => __('Category'),
      );
      $args = array(
        'labels' => $labels,
        'public' => true,
        'publicly_queryable' => true,
        'show_ui' => true, //false - to hide from the admin area menu
        'rewrite' => true,
        'query_var' => true,
        'capability_type' => 'post',
        'hierarchical' => true, //allow parent pages
        'show_in_nav_menus' => false,
        'menu_position' => 1000,
        'supports' => array(
          'title',
              'page-attributes'
        )
      );
      register_post_type('Category',$args);
    }

    /* Product Post Type */
    add_action('init', 'Product_post_type_init');
    function Product_post_type_init() {
      $labels = array(
        'name' => _x('Product', 'post type general name'),
        'singular_name' => _x('Product', 'post type singular name'),
        'add_new' => _x('Add New', 'Product'),
        'add_new_item' => __('Add New Product'),
        'edit_item' => __('Edit Product'),
        'new_item' => __('New Product'),
        'view_item' => __('View Product'),
        'search_items' => __('Search Products'),
        'not_found' =>  __('No Products found'),
        'not_found_in_trash' => __('No Products found in Trash'),
      );
      $args = array(
        'labels' => $labels,
        'public' => true,
        'publicly_queryable' => true,
        'show_ui' => true, //false - to hide from the admin area menu
        'rewrite' => true,
        'query_var' => true,
        'capability_type' => 'post',
        'hierarchical' => true, //allow parent pages
        'show_in_nav_menus' => false,
        'menu_position' => 1000,
        'supports' => array(
          'title',
		  'editor',
              'page-attributes'
        )
      );
      register_post_type('Product',$args);
    }

Thanks