Some fixes of Warning or Notice in rare situations.
A new Widget category class (with new Walker) for adapted numbering according current language. This new Widget must be registered by webmaster in his theme via few line of code. Because it is a new widget named ©xili Widget, you must set it via the Appearance/Widgets settings page (and remove default Categories widget) 😉

// ...inside function twentyfifteen_xilidev_setup - at end of condition if xili-language exists (to avoid error if desactivated)
add_action( 'widgets_init', 'twentyfifteen_xili_add_widgets' );
// ...
}
add_action( 'after_setup_theme', 'twentyfifteen_xilidev_setup', 11 );

function twentyfifteen_xili_add_widgets () {
    register_widget( 'xili_Widget_Categories' ); // in xili-language-widgets.php since 2.16.3
}

Widget “Archives” is improved (through filtering) to display only months with posts of target/displayed languages. It is recommended to reset cache by adding a post.