Proposition 5

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

Algebra, chapter X, § 7. Produit de composition

Let

(\mathscr{E})\qquad 0\longrightarrow M'\xrightarrow{\,f\,}M\xrightarrow{\,g\,}M''\longrightarrow0

be an exact sequence of left $A$ -modules, $\theta\in\operatorname{Ext}^1_A(M'',M')$ the associated class, $N$ a left $A$ -module, $n$ an integer.

a) The connecting homomorphism $\delta^n(N,\mathscr{E}):\operatorname{Ext}^n_A(N,M'')\longrightarrow\operatorname{Ext}^{n+1}_A(N,M')$ is the composition product $\alpha\mapsto\theta\circ\alpha$ with $\theta$ .

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

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