Corollary 3

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

Algebra, chapter X, § 4. Produits de torsion

Let $C'$ be a complex of left $A$ -modules such that $B(C')$ and $H(C')$ are projective. For every complex $C$ of right $A$ -modules, the mapping $\gamma(C,C')$ is bijective.

Indeed, $C'$ is split (X, p. 35, example 4) and $H(C')$ is projective; therefore we can apply corollary 1.

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

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Cites

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