Lemma 13.40.3. Let $\mathcal{D}$ be a triangulated category. Consider Postnikov systems for complexes of length $n$.

For $n = 0$ Postnikov systems always exist and any morphism (13.40.1.1) of complexes extends to a unique morphism of Postnikov systems.

For $n = 1$ Postnikov systems always exist and any morphism (13.40.1.1) of complexes extends to a (nonunique) morphism of Postnikov systems.

For $n = 2$ Postnikov systems always exist but morphisms (13.40.1.1) of complexes in general do not extend to morphisms of Postnikov systems.

For $n > 2$ Postnikov systems do not always exist.

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