what are fields_for for?

I have:

class Company < ActiveRecord::Base
  has_many :categorizations
  has_many :categories, :through => :categorizations

rails c

irb(main):003:0> comp=Company.find 1
  Company Load (2.0ms) SELECT "companies".* FROM "companies" WHERE
"companies"."id" = 1 LIMIT 1
=> #<Company id: 1, name: "company-1", vat_number: "11111111112",
fiscal_code: "1111111111111112", address: "company-1", street_number:
"1", zip_code: "11112", city: "company-1", prov: "CA",
elected_address: "", elected_street_number: "", elected_zip_code: "",
elected_city: "", elected_prov: "", tel: "", fax: "", email: "",
website: "", reports: "prova", notes: "", created_at: "2012-01-16
10:19:16", updated_at: "2012-01-16 11:43:40">

rb(main):004:0> comp.categorizations
  Categorization Load (1.0ms) SELECT "categorizations".* FROM
"categorizations" WHERE "categorizations"."company_id" = 1
=> [#<Categorization id: 101, company_id: 1, category_id: 1,
classification_id: nil, amount: nil, created_at: "2012-01-17
08:31:41", updated_at: "2012-01-17 08:31:41">, #<Categorization id: 1,
company_id: 1, category_id: 2, classification_id: nil, amount:
#<BigDecimal:7b4b3d0e,'4.0',1(4)>, created_at: "2012-01-16 10:19:17",
updated_at: "2012-01-17 08:56:42">]

As you see comp has two categorizations.

In the form I have:

= semantic_form_for @company do |f|
  = f.inputs do
    = f.input :categories, :input_html => { :multiple => true, :id => "cat"}
  = f.inputs :name, :vat_number, :fiscal_code, :city, :prov, :address,
:street_number, :elected_zip_code, :elected_city
  = f.inputs :elected_prov, :elected_address, :elected_street_number,
:tel, :fax, :email, :website, :reports, :notes
  = semantic_fields_for :categorizations do |cat|
    = cat.inputs :id

I would expect to see the two categorizations id, instead I see nothing.
Does not fields_for iterate over categorizations fields and show their values?