We discuss the inverse problem of determining a Poisson algebra as a classical limit from some Lie algebra as a quantized space. There exists a category of quantization that contain quantizations as the morphisms and Poisson algebras and Lie algebras as the objects. We formulate the classical limit within the category. From a Lie algebra, we construct a sequence of quantized spaces, from which we determine a Poisson algebra by a classical limit as the category theory. We present a method to obtain this sequence of the quantizations from the principle of least action by using a kind of matrix model.