Abstract: We will present the first step of a research program aimed at understanding Kontsevich's quantization formula from a functorial and geometrical point of view. In this talk, we will focus on construction of a local version of Weinstein extended symplectic category, which is a true category in contrast to the later. Some results linking this new category with Kontsevich's star-product support the hope that this is the right framework to define a quantization functor.