2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71754In this paper we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Ext-groups. In appendix we prove the existence of miniversal derived deformations of complexes.22 pagesK-Theory and HomologyCategory Theory13D10; 18E30; 18G35text