Corollary 1

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

If $\mathrm{Tor}_1^A(M, N'') = 0$ , the sequence

0 \longrightarrow M \otimes_A N' \xrightarrow{1 \otimes u} M \otimes_A N \xrightarrow{1 \otimes v} M \otimes_A N'' \longrightarrow 0

is exact.

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

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