Classification of holomorphic vector bundles on noncommutative two-tori

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We prove that every holomorphic vector bundle on a noncommutative two-torus T can be obtained by successive extensions from standard holomorphic bundles considered in math.QA/0211262. This implies that the category of holomorphic bundles on T is equivalent to the heart of certain t-structure on the derived category of coherent sheaves on an elliptic curve.