A framework is given for defining and comparing factorizability theories (as used, for example, to relate modules over the group rings of finite groups). The strict theory of Fröhlich [4] and the Hecke theory of [7] as well as several other related theories are shown to be equivalent. Of particular interest among the several equivalent theories examined is that of normaliser factorizability. This is perhaps the most user friendly theory and follows most closely the framework of the classical theory. Among other tools, the theory of permutation projectives and their species is used.