Lemma 1

Tag 0E2H, permanent. Cite it as [Bourbaki, Tag 0E2H].

Algebra, chapter X, § 9. Complexes de Koszul

If the complex $C$ is zero on the right (resp. on the left), then $\mathbf{K}^A(u, C)$ (resp. $\mathbf{K}^*_A(u, c)$ ) is zero on the right (resp. on the left), and $\gamma_0$ (resp. $\lambda^0$ ) is bijective.

This follows from X, p. 62, prop. 1 and p. 82, prop. 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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