Quantization as a functor

Can anyone give an mathematical elaboration of the following statement:

Quantization is a functor carrying the category of Hilbert space and linear maps to that of Symplectic manifolds satisfying some conditions specified by laws of Physics.

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–  Qmechanic May 25 at 9:23
where is that statement taken from? –  Prathyush May 25 at 13:41
That's not quantization. The direction is backwards. –  user1504 May 25 at 16:05
See also Geometric Quantization, and a article by John Baez –  Trimok May 27 at 10:20