Definition 3

Tag 0DX6, permanent. Cite it as [Bourbaki, Tag 0DX6].

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

One calls connecting homomorphism of extension modules relative to the exact sequence $(\mathscr{F})$ and to the module $N$ , the composite homomorphism

\delta(\mathscr{F}, N) : \overline{\varphi}_N(M'') \circ \partial(\mathscr{F}_N) \circ \overline{\varphi}_N(M')^{-1} : \mathrm{Ext}_A(M', N) \to \mathrm{Ext}_A(M'', N).

It is a graded

k

-homomorphism of ascending degree 1, whose homogeneous components are denoted

\delta^n(\mathscr{F}, N) : \mathrm{Ext}_A^n(M', N) \to \mathrm{Ext}_A^{n+1}(M'', N)

. One then proves as above the following statements:

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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