How to get the ancestors of a category from the Group page?

Here’s the story:
Each Category has an auto-generated Group, and they’re related to each other 1-to-1 via the category_custom_fields “group_id” and group_custom_fields “category_id”.

I’ve added a Category to a group thusly:

  add_to_serializer :basic_group, :category do
    Category.find_by(id: object.custom_fields["category_id"])

Now on the Group’s page (/g/GroupName), I want to make it look like just another Category page (e.g. Latest, New, Unread, Top) where it has the bread crumbs. Something like this:

Problem is, from the group page, my newly-added group.category seems to be missing some values needed, like category.ancestors needed by categoryBreadcrumbs, and can_edit needed for showing the edit icon. Also, category custom fields are not serialized in the group.category.

Does anyone have any tips on how to get the Category breadcrumbs to work on the Group page?