Good morning Howard,
also for us the desire to have courses show up in several categories arose when thinking about using one category for each Department. There are some courses that are shared between Departments.
I don't think the intelligent linking to groups that you suggest is necessary. If a course is used by students from several faculties then they may well be in different groups, but which group a student is in should have nothing to do with which link they used to reach the course page.