Chorny, Boris2016-03-152016-03-150002-9939http://hdl.handle.net/1885/100252We show that the model category of diagrams of spaces generated by a proper class of orbits is not cofibrantly generated. In particular, the category of maps between spaces may be supplied with a non-cofibrantly generated model structure.The author was a fellow of the Marie Curie Training Site hosted by the Centre de Recerca Matem`atica (Barcelona), grant no. HPMT-CT-2000-00075 of the European Commission.© 2003 American Mathematical SocietyModel categoryequivariant homotopynon-cofibrantly generated2003-02-1110.1090/S0002-9939-03-06901-6