Outputs a category breadcrumb with a parent/child relationship. This code will only work flawlessly if there is only one category selected on the post.

category-breadcrumb.php

<?php
function somesite_cat_breadcrumb() {
  	// variables
	$category = get_the_category();
	$catParID = $category[0]->category_parent;
	$catParent = get_cat_name($catParID);
	$catName = $category[0]->cat_name;

	// filter breadcrumb for posts with no parent categories versus those with 1 or more parent categories and
	// then display the immediate parent category (if applicable) followed by the current (or first) post category
	if( $catParID == 0 ) { 
		echo '<span>'.$catName.'</span>';
	} else {
		// category breadcrumb output
		echo '<a href="'.get_category_link($catParID).'">'.$catParent.'</a>'; 
		echo ' / ';
		echo '<span>'.$catName.'</span>';
	}
}
?>