A hermitian analogue of the Morita theorems

ABSTRACTLet F1 be an equivalence of type I between two categories of modules with hermitian forms. In other words, suppose F is an equivalence between the two underlying categories of modules, and F1 is an equivalence, given by F1(M,h)=(F(M),hF1) and F1(f) = F(f), such that the non-singularity of a free hyperbolic module of hyperbolic rank 1 is preserved by F1. Then every equivalence generated by a set of hermitian Morita equivalence data is of type I and every equivalence of type I arises from a set of hermitian Morita equivalence data.