A Generalization of the Quantization of Poisson Manifolds

Abstract

We propose a unified perspective of quantization using a categorical approach. From a fixed Poisson algebra, we define quantization categories as subcategories of the $R$-module category equipped with the structure of classical limits. The generalized quantization categories have a huge structure including matrix regularization, strict deformation quantization, prequantization, Poisson enveloping algebra and so on.