2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155623In this paper, we show all k-linear abelian 1-Calabi-Yau categories over an algebraically closed field k are derived equivalent to either the category of coherent sheaves on an elliptic curve, or to the finite dimensional representations of k[[t]]. Since all abelian categories derived equivalent with these two are known, we obtain a classification of all k-linear abelian 1-Calabi-Yau categories up to equivalence.12 pages, as accepted by the International Mathematics Research NoticesCategory Theory18E10; 18E30text