T-structures on unbounded twisted complexes

Abstract This paper is a sequel to T-structures and twisted complexes on derived injectives by the same author with W. Lowen M. Van den Bergh. We define dg-category of unbounded dg-category, which particularly interesting in case dg-categories or projectives associated t-structure. On such we natural “injective” dually “projective” intended as direct generalization homotopy categories injective projective objects an abelian category.