Corollary

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

If $R$ is a flat resolution of $M$ , the homomorphism

\psi(P,R):\operatorname{Tor}^A(P,M)\longrightarrow H(P\otimes_A R)

is bijective. If $R$ is a projective resolution of $M$ , the homomorphism

\varphi(R,N):H(\operatorname{Homgr}_A(R,N))\longrightarrow \operatorname{Ext}_A(M,N)

is bijective. If $E$ is an injective resolution of $N$ , the homomorphism

\varphi(M,E):H(\operatorname{Homgr}_A(M,E))\longrightarrow \operatorname{Ext}_A(M,N)

is 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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