Bourbaki

Corollaire 1

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

Algebra, chapter X, § 7. Produit de composition

a) The connecting homomorphism HomA(M′′,M′′)→ExtA1(M′′,M′)\mathrm{Hom}_A(M'', M'') \to \mathrm{Ext}_A^1(M'', M') sends 1M′′1_{M''} to θ\theta.

b) The connecting homomorphism HomA(M′,M′)→ExtA1(M′′,M′)\mathrm{Hom}_A(M', M') \to \mathrm{Ext}_A^1(M'', M') sends 1M′1_{M'} to −θ-\theta.

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

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Translated with machine help, not yet reviewed by a person.