Example 5

Tag 0DS4, permanent. Cite it as [Bourbaki, Tag 0DS4].

Algebra, chapter X, § 2. Complexes de A-modules

In particular, if A is principal, a free complex $C$ is split if and only if $H(C)$ is free (that is to say $H_n(C)$ free for every $n\in\mathbf{Z}$ ).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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