Corollary 3

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

Algebra, chapter X, § 5. Modules d’extensions

Let $M$ be a projective $A$ -module (resp. an injective $A$ -module). For every complex $C$ of $A$ -modules and every integer $n$ , the canonical homomorphism

H^n(\mathrm{Homgr}_A(M, C)) \to \mathrm{Hom}_A(M, H^n(C))

(resp. $H^n(\mathrm{Homgr}_A(C, M)) \to \mathrm{Hom}_A(H_n(C), M)$ ) is bijective.

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

Cited by

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Cites

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