This function returns an array consisting of a hierarchy tree of categories. It has one required parameter, the category group_id. The category group(s) may be defined as a pipe delimited list of group_ids or an array. The second parameter allows the specification of any selected categories (useful when used as form data), while the third parameter determines the ordering of the categories (a for alphabetical based on category_name or c for the specified custom ordering):

ee()->api_channel_categories->category_tree(
    (mixed) $group_id, [(mixed) $selected, [(string) c or a]]
);

Example of returned data:

array(
    0 => array(
        '0' =>  (int) Category ID,
        '1' =>  (string) Category Name,
        '2' =>  (int) Category Group ID,
        '3' =>  (string) Category Group Name,
        '4' =>  (bool) Selected,
        '5' =>  (int) Depth Nested in the Tree,
        '6' =>  (int) Category Parent ID
    ),
    1 => array(...)
);

This function returns an array consisting of a hierarchy tree of categories formatted for use in select and multi-select forms and related javascript. It takes 3 optional parameters. The first parameter determines whether the returned categories are arranged in a nested format. The second parameter allows you to specify categories to include or exclude from the array. Included categories may be in the format of an array of category ids. You may also include or exclude categories using a pipe delimited string. This parameter defaults to (bool) FALSE, which will include all categories. The third parameter determines the site_id, and may be in the format of an array of site ids. You may also include or exclude sites using a pipe delimited string. This parameter defaults to (bool) FALSE, which will include only categories from the current site:

ee()->api_channel_categories->category_form_tree(
    [(string) $nested y/n, [(mixed) $categories, [(mixed) $sites]]]
);

Example of returned data:

array(
    0 => array(
        '0' =>  (int) Category Group ID,
        '1' =>  (int) Category ID,
        '2' =>  (string) Category Name in ASCII Format,
        '3' =>  (int) Parent ID
    ),
    1 => array(...)
);

This function finds the parents of the specified categories and adds them to the cat_parents class variable:

ee()->api_channel_categories->fetch_category_parents(
    (array) $cat_array
);

Given an array or a pipe delimited list of category group ids, this returns an array of the category group names if the user has permission to administrate channels or edit categories. Returns FALSE otherwise:

ee()->api_channel_categories->fetch_allowed_category_groups(
    (mixed) $cat_group
);

Example Usage:

$group_id = '1|5';

$allowed = ee()->api_channel_categories->fetch_allowed_category_groups($group_id);

if ($allowed != FALSE) {
    foreach($allowed as $val)
    {
        echo 'Group ID: '.$val['0'].' Group Name: '.$val['1'].'';
    }
}