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Given a triangulated 2-Calabi-Yau category C and a cluster-tilting subcategory T , the index of an object X of C is a certain element of the Grothendieck group of the additive category T . In this note, we show that a rigid object of C is determined by its index, that the indices of the indecomposables of a cluster-tilting subcategory T form a basis of the Grothendieck group of T and that, if T and T are related by a mutation, then the indices with respect to T and T are related by a certaindoi:10.1093/imrn/rnn029 fatcat:e53acqfhpfgdhdb657xcdl7wni