i am not sure but try this:
query_posts('category_name=". $category[0]->cat_name);
if (have_posts()) : while (have_posts()) : the_post();
$posttags = get_the_tags();
if ($posttags) {
foreach($posttags as $tag) {
$all_tags_arr[] = array($tag->name,wp_basename(get_permalink()));
}
}
endwhile; endif;
foreach ($all_tags_arr as $cat_by_tag) {
$output_promotion .= "<li><a href="' . get_bloginfo('url'). "https://wordpress.stackexchange.com/" . $cat_by_tag[1] . "https://wordpress.stackexchange.com/">'. $cat_by_tag[0] .'</a></li>';
}
print_r($output_promotion);