Why does only one of my has_many though models work - ruby-on-rails

Question

I followed http://railscasts.com/episodes/17-habtm-checkboxes-revised?view=asciicast tutorial to set up a has_many through relationship and when I try to access information from one model it works but not from the other.
I can access the Category information from the Product model via #product.category_ids and #product.categories, but the reverse isn't true. I can't access the Product information from the Category model. Using #category.product_ids or #category.products gives me the error NoMethodError: undefined method 'product_ids' for #<Category:0x007fa70d430e98>
Product.rb
class Product < ActiveRecord::Base
attr_accessible :category_ids
has_many :categorizations
has_many :categories, through: :categorizations
accepts_nested_attributes_for :categorizations, :allow_destroy => true
end
Category.rb
class Category < ActiveRecord::Base
attr_accessible :product_ids
has_many :categorizations
has_many :products, through: :categorizations
end
-- EDIT --
Schema.rb
ActiveRecord::Schema.define(:version => 20130926192205) do
create_table "categories", :force => true do |t|
t.string "name"
t.datetime "created_at", :null => false
t.datetime "updated_at", :null => false
end
create_table "products", :force => true do |t|
t.string "name"
t.datetime "created_at", :null => false
t.datetime "updated_at", :null => false
end
create_table "categorization", :force => true do |t|
t.integer "product_id"
t.integer "category_id"
t.datetime "created_at", :null => false
t.datetime "updated_at", :null => false
end
add_index "categorization", ["product_id", "category_id"], :name => "index_categorization_on_product_id_and_category_id", :unique => true
add_index "categorization", ["product_id"], :name => "index_categorization_on_product_id"
add_index "categorization", ["category_id"], :name => "index_categorization_on_category_id"
end

Answer 1

To access the records from each object you should be able to:
#category.products
and
#product.categories
That will give you the associated objects.
product_ids is not a attribute on a category and it does not have accepts_attributes_for :products like your category model so removing attr_accessible :product_ids should fix the error.