2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77297We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (A, A*) is a Lie bialgebroid; (3) that a vacant double Lie algebroid structure is equivalent to a matched pair structure on the side Lie algebroids.19 pages, LaTeXDifferential Geometry58H05 (primary) 17B66, 18D05, 22A22, 58F05text