List categories for author: list_categories function inside list_authors function

Seemed interesting, so here is my version. Not sure about get_user_by(), should be more robust way to get objects for authors.

function my_list_authors() {

    $authors = wp_list_authors( array(
    'exclude_admin' => false,
    'html' => false,
    'echo' => false
    ) );

    $authors = explode( ',', $authors );

    echo '<ul>';

    foreach ( $authors as $author ) {

    $author = get_user_by( 'login', $author );
    $link = get_author_link( false, $author->ID );
    echo "<li><a href="https://wordpress.stackexchange.com/questions/813/{$link}">{$author->display_name}</a><ul>";

    $posts = get_posts( array(
        'author' => $author->ID,
        'numberposts' => -1
    ) );

    $categories = array();

    foreach ( $posts as $post )
        foreach( get_the_category( $post->ID ) as $category )
        $categories[$category->term_id] =  $category->term_id;

    $output = wp_list_categories( array(
        'include' => $categories,
        'title_li' => '',
        'echo' => false
        ) );

    echo $output . '</ul></li>';
    }

    echo '</ul>';
}