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This note gives a one-to-one correspondence between the equivalence classesof a certain type of 2-dimensional Calabi-Yau categories, and certain type ofquivers, This is an analogue of the result in Stability structures, motivicDonaldson-Thomas invariants and cluster transformations, arXiv: 0811.2435, byM. Kontsevich, Y. Soibelman.

Correspondence between 2 Calabi-Yau Categories and Quivers