Proposition 5

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

The $k$ -homomorphisms

\begin{aligned} & \psi_M(N) : \mathrm{Tor}^A(M, N) \to H(L(M) \otimes_A N) \\ & \overline{\psi}_N(M) : \mathrm{Tor}^A(M, N) \to H(M \otimes_A L(N)) \end{aligned}

are 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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