UPDATE: According to the task to get the browseable categories for the Albums app, the MySQL query foe the object categories should have the following look:

INSERT INTO `sys_objects_category` SET

`object` = 'my_custom_category',

`search_object` = 'bx_albums',

`form_object` = 'bx_albums',

`list_name` = 'Albumcat',

`table` = 'bx_albums_albums',

`field` = 'albumcat',

`join` = 'INNER JOIN `sys_profiles` ON (`sys_profiles`.`content_id` = `bx_albums_albums`.`author`)',

`where` = 'AND `sys_profiles`.`status` = ''active''',

`override_class_name`= '', 

`override_class_file` = '';