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We propose a generalization of quantization as a categorical way. For a fixedPoisson algebra quantization categories are defined as subcategories ofR-module category with the structure of classical limits. We construct thegeneralized quantization categories including matrix regularization, strictdeformation quantization, prequantization, and Poisson enveloping algebra,respectively. It is shown that the categories of strict deformationquantization, prequantization, and matrix regularization with some conditionsare categorical equivalence. On the other hand, the categories of Poissonenveloping algebra is not equivalent to the other categories.

Categorical Perspective on Quantization of Poisson Algebra