I am looking for a function to create category links in the wordpress loop for articles

You can use this for single category name with link:

$category = get_the_category(); 
echo '<a href="'.get_category_link($category[0]->cat_ID).'"><img src="'.$category[0]->cat_name.'" alt="'.$category[0]->cat_name.'" /></a>';

Or for the loop you can try this:

foreach(get_the_category() as $category){
    echo '<a href="'.get_category_link($category->cat_ID).'"><img src="'.$category->cat_name.'" alt="'.$category->cat_name.'" /></a>';
}