Get Category Slug

Is there a way to retrieve the category slug? I would like to use it in place of <?php echo $category_nicename; ?> below.

<?php if (is_home())
      query_posts("showposts=10&cat=3");
?>
	<?php if (have_posts()) :?>
	<?php
	$category = $wp_query->get_queried_object();
	$cat_name = $category->name;
	?>
    <div class="right_header"><span class="right_header_text"><a href="<?php echo get_settings('home'); ?>/index.php/category/<?php echo $category_nicename; ?>"><?php echo $cat_name; ?></a></span></div>