Let _RC_S be a semidualizing (R,S)-bimodule. Then _RC_S induces an equivalent between the Auslander class A_C (S) and the Bass class B_C (R). Let A and B
be free normalizing extensions of R and S respectively. In this paper, we prove that
HomS(_BB_S,_RC_S) is a semidualizing (A,B)-bimodule under some suitable conditions,
and so HomS(_BB_S,_RC_S) induces an equivalence between the Auslander class
A_{HomS (BBS,RCS )}(B)
and the Bass class
B_{HomS (BBS,RCS )}(A).
Furthermore, under a suitable condition on _RC_S, we develop a generalized Morita theory
for Auslander categories