Corollary 1

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

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

If two of the complexes $C$ , $C'$ , $C''$ have zero homology, the third one does also. For $u$ (resp. $v$ *) to be a homomorphism, it is necessary and sufficient that* $C''$ (resp. $C'$ *) have zero homology. For $\partial(u,v)$ to be bijective, it is necessary and sufficient that $C$ have zero homology.

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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