By the SYZ construction, a mirror pair (X, ?X) of a complex torus X and a mirror partner X? of the complex torus X is described as the special Lagrangian torus fibrations X-+ B and X?-+ B on the same base space B. Then, by the SYZ transform, we can construct a simple projectively flat bundle on X from each affine Lagrangian mul-tisection of X?-+ B with a unitary local system along it. However, there are ambiguities of the choices of transition functions of it, and this causes difficulties when we try to con-struct a functor between the symplectic geometric category and the complex geometric category. In this paper, we prove that there exists a bijection between the set of the iso-morphism classes of their objects by solving this problem.
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