Library. A library includes:
(1) A public library;
(2) A public elementary school or secondary school library;
(3) An academic library;
(4) A research library, which for the purpose of this section means a library that:
(i) Makes publicly available library services and materials suitable for scholarly research and not otherwise available to the public; and
(ii) Is not an integral part of an institution of higher education; and
(5) A private library, but only if the state in which such private library is located determines that the library should be considered a library for the purposes of this definition.