Corollary 2

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

Algebra, chapter X, § 5. Modules d’extensions

If $B(C)$ and $Z(C)$ are projective, one has, for every $A$ -module $N$ and every integer $n$ , a split exact sequence:

(13) $0 \longrightarrow \mathrm{Ext}_A^1(H_{n-1}(C), N) \xrightarrow{\beta^n} H^n(\mathrm{Homgr}_A(C, N)) \xrightarrow{\lambda^n} \mathrm{Hom}_A(H_n(C), N) \longrightarrow 0$ .

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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