Category of quantizations and inverse problem

We introduce a category composed of all quantizations Poisson algebras. By the category, we can treat in unified way various for algebras and develop new classical limit formulation. This formulation proposes method inverse problem, that is, problem finding from quantized space. Equivalence is defined by using this conditions under which two are equivalent investigated. Two types limits as context theory, they determined giving sequence objects. Using these limits, discuss determining some noncommutative Lie algebra. From algebra, construct spaces, determine also present to obtain principle least action matrix regularization. Apart above algebras, fixed single algebra introduced. In other defined, it automatically category.