Rewriting Core Variable Using functions.php

I want to rewrite a wordpress core varaible on wp-includes/category-template.php line 163
$rel = ( is_object( $wp_rewrite ) && $wp_rewrite->using_permalinks() ) ? 'rel="category tag"' : 'rel="category"';
I want to use functions.php within my theme files to overwrite this variable. I’ve added a filter

add_filter('get_the_category_list', 'rewrite_rel' );

But I am stuck on the function portion, need help! Below is what I have

function rewrite_rel($result, $show) {
switch ($show) {
case 'rel':
$return = ( is_object( $wp_rewrite ) && $wp_rewrite->using_permalinks() ) ? 'rel="chapter"' : 'rel="chapter"';
break;
default:
}
return $result;
}