I've modified your code a bit, but now you have an array of tag id's which you can use for any purpose, for ex. list added below.
if (is_category()){
$cat = get_query_var('cat');
$yourcat = get_category ($cat);
}
$tag_IDs = array();
query_posts('category_name='.$yourcat->slug);
if (have_posts()) : while (have_posts()) : the_post();
$posttags = get_the_tags();
if ($posttags):
foreach($posttags as $tag) {
if (!in_array($tag->term_id , $tag_IDs)):
$tag_IDs[] = $tag->term_id;
$tag_names[$tag->term_id] = $tag->name;
endif;
}
endif;
endwhile; endif;
wp_reset_query();
echo "<ul>";
foreach($tag_IDs as $tag_ID){
echo '<a href="'.get_tag_link($tag_ID).'">'.$tag_names[$tag_ID].'</a>';
}
echo "</ul>";