Why is it not good to have a primary key on a join table?

Question

I was watching a screencast where the author said it is not good to have a primary key on a join table but didn't explain why.

The join table in the example had two columns defined in a Rails migration and the author added an index to each of the columns but no primary key.

Why is it not good to have a primary key in this example?

create_table :categories_posts, :id => false do |t|
  t.column :category_id, :integer, :null => false
  t.column :post_id, :integer, :null => false
end
add_index :categories_posts, :category_id
add_index :categories_posts, :post_id

EDIT: As I mentioned to Cletus, I can understand the potential usefulness of an auto number field as a primary key even for a join table. However in the example I listed above, the author explicitly avoids creating an auto number field with the syntax ":id => false" in the "create table" statement. Normally Rails would automatically add an auto-number id field to a table created in a migration like this and this would become the primary key. But for this join table, the author specifically prevented it. I wasn't sure why he decided to follow this approach.

Answer 1

Some notes:

1. The combination of category_id and post_id is unique in of itself, so an additional ID column is redundant and wasteful
2. The phrase "not good to have a primary key" is incorrect in the screencast. You still have a Primary Key -- it is just made up of the two columns (e.g. CREATE TABLE foo( cid, pid, PRIMARY KEY( cid, pid ) ). For people who are used to tacking on ID values everywhere this may seem odd but in relational theory it is quite correct and natural; the screencast author would better have said it is "not good to have an implicit integer attribute called 'ID' as the primary key".
3. It is redundant to have the extra column because you will place a unique index on the combination of category_id and post_id anyway to ensure no duplicate rows are inserted
4. Finally, although common nomenclature is to call it a "composite key" this is also redundant. The term "key" in relational theory is actually the set of zero or more attributes that uniquely identify the row, so it is fine to say that the primary key is category_id, post_id
5. Place the MOST SELECTIVE column FIRST in the primary key declaration. A discussion of the construction of b(+/*) trees is out of the scope of this answer ( for some lower-level discussion see: http://www.akadia.com/services/ora_index_selectivity.html ) but in your case, you'd probably want it on post_id, category_id since post_id will show up less often in the table and thus make the index more useful. Of course, since the table is so small and the index will be, essentially, the data rows, this is not very important. It would be in broader cases where the table is wider.