yes you can do that. You can use get_category_link for it.
if():
while():
the_content();
if(category == "category one"){
// Get the ID of a given category
$category_id = get_cat_ID( 'helper for category one' ); //get_cat_ID('category_name');
// Get the URL of this category
$category_link = get_category_link( $category_id );
// Print category link here
}
else{
display_nothink
}
endif;
endwhile;
endif;
You can also use action/filter if you dont have direct access to single.php file