It may be something to do with the object? 

Did you cannt seem your categorized Groups on Categories list page or you cannt seem category' attribute in Groups subtext on Search page like

My Group
Some text
Tags: elgg

Category: --missing--
just now

?

Any way add in views\default\group\default.php

$categories = elgg_view('output/categories', $vars);

Then display it for non-full viewing in subtile section:

'subtitle' => $group->briefdescription . $categories,

BTW, see on https://github.com/Elgg/community_groups

Thank you again, RvR :) It now shows the category in the subtitle. When I click the category, I am taken to this page http://www.oyeahub.com/e/categories/list?category=Health+%26amp%3B+Wellness. It is a "list?" search page.

However, the group doesn't display on this page. It shows no results for the tag. 

It's a categories' list page.

Try to add in categories\pages\categories\listing.php :

Line 13   $type = get_input("type", 'object');

Line 14   $type .= "group";

No luck. I cannot seem have the group show on the list page. Wish it was easier. 

I haven't looked at it, but I believe the code for categories only targets objects, so even if you put the categories input on the group edit page the categories inputs won't be saved... you'll need to add hooks for group create/update to attach the categories metadata

@Eric Schilling Works with it:

$params = array(
    'metadata_name' => 'universal_categories',
    'metadata_value' => $category,
    'type' => $type,
    'subtype' => $subtype,
    'owner_guid' => $owner_guid,
    'limit' => $limit,
    'full_view' => FALSE,
    'metadata_case_sensitive' => FALSE,
);

$params2 = array(
        'metadata_name' => 'universal_categories',
        'metadata_value' => $category,
        'type' => 'group',
        'full_view' => FALSE,
    );

$objects = elgg_list_entities_from_metadata($params);

$objects .= elgg_list_entities_from_metadata($params2);

Bravo, RvR! It works!