2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161868By inspiring ourselves in Drinfeld's DG quotient, we develop Postnikov towers, k-invariants and an obstruction theory for dg categories. As an application, we obtain the following `rigidification' theorem: let A be a homologically connective dg category and F:B -> H0(A) a dg functor to its homotopy category. If the family of obstruction classes vanishes, then a lift for F exists.27 pagesK-Theory and HomologyAlgebraic Topology55S45, 55S35 (Primary); 18G55, 18D20 (Secondary)text