simple dynamic body ID/class

In functions.php, I’ve implemented something like this:

function bodystyle() {
	global $post;
	$postclass = $post->post_name;

	if (is_home()) {
	echo 'id="home"';
	} elseif (is_single()) {
	echo 'id = "single" class="' . $postclass . '"';
	} elseif (is_search()) {
	echo 'id="search"';
	} elseif (is_archive()) {
	echo 'id="archive"';
	} elseif (is_page()) {
	echo 'id="page" class="' . $postclass . '"';
	}
}

How would I add another conditional (is_category) that returns the name of the category as a class, similar to what I’ve already done for single-posts and pages?