Remark 4

Tag 0DY7, permanent. Cite it as [Bourbaki, Tag 0DY7].

Algebra, chapter X, § 6. Utilisation de résolutions non canoniques

If R is projective or if E, E', E'' are injective, the sequence (7) is exact ( $\lambda$ , p. 83, Prop. 2); moreover, $\varphi(R, E'')$ is bijective (Th. 1); hence

\delta(M, (5)) = \varphi(R, E') \circ \partial((7)) \circ \varphi(R, E'')^{-1}.

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

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