Uniqueness of dg‐lifts via restriction to injective objects

Abstract We prove a uniqueness result of dg‐lifts for the derived pushforward and pullback functors of a flat morphism between separated Noetherian schemes, between the unbounded or bounded below derived categories of quasi‐coherent sheaves. The technique is purely algebraic‐categorical and involves reconstructing dg‐lifts uniquely from their restrictions to the subcategories of injective objects.