Does anybody know, how to remove a ManyToMany relationship ?

I've experimented with the follwoing case:

@Entity
@Table (name="products")
public class A_Product implements Serializable {
 private int id;

 A_Product() {}

 @Column (name ="products_id", nullable=false)
 @Id(generate = GeneratorType.IDENTITY)
 public int getId() { id }
 void setId(int id) { this.id = id; }

 @ManyToMany(cascade = {CascadeType.PERSIST, CascadeType.MERGE},
 fetch = FetchType.LAZY, mappedBy="products")
 public Collection<A_Category> getCategories() { return categories; }

 void setCategories(Collection<A_Category> categories) { this.categories = categories; }
 }

@Entity
@Table(name="categories")
public class A_Category implements Serializable {
 private int id;
 @Id(generate = GeneratorType.IDENTITY)
 @Column(name="categories_id", nullable=false)
 public int getId() { return this.id; }
 public void setId(int id) { this.id = id; }

 @ManyToMany(cascade = { CascadeType.PERSIST, CascadeType.MERGE },
 fetch = FetchType.EAGER)
 @AssociationTable(table = @Table(name="products_to_categories"),
 joinColumns = {
 @JoinColumn(name="categories_id", referencedColumnName="categories_id")
 },
 inverseJoinColumns = {
 @JoinColumn(name="products_id", referencedColumnName="products_id")
 })
 public Collection<A_Product> getProducts() { return products; }
 void setProducts(Collection<A_Product> products) { this.products = products; }
}

@Stateless
class ProductManager {
 @Inject
 private EntityManager manager;
 // ...
 @TransactionAttribute(value = TransactionAttributeType.REQUIRES_NEW)
 public void delete(A_Product product, String clientID) {
 if (product == null) { return false; }
 manager.refresh(product);
 Collection<A_Category> cats = product.getCategories();
 for (A_Category c : cats) {
 c.getProducts().remove(product);
 manager.merge(c);
 }
 manager.remove(product);
 }
}

Query q = manager.createQuery("DELETE FROM products_to_categories ptc "
 + "WHERE ptc.products_id=:id").setParameter("id", product.getId());
 q.executeUpdate();