Proposition 22.10.3. Let (A, \text{d}) be a differential graded algebra. The homotopy category K(\text{Mod}_{(A, \text{d})}) of differential graded A-modules with its natural translation functors and distinguished triangles is a triangulated category.
Proof. We know that K(\text{Mod}_{(A, \text{d})}) is a pre-triangulated category. Hence it suffices to prove TR4 and to prove it we can use Derived Categories, Lemma 13.4.15. Let K \to L and L \to M be composable morphisms of K(\text{Mod}_{(A, \text{d})}). By Lemma 22.7.5 we may assume that K \to L and L \to M are admissible monomorphisms. In this case the result follows from Lemma 22.10.2. \square
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