Proposition 9

Tag 0E0D, permanent. Cite it as [Bourbaki, Tag 0E0D].

The following diagram, where $\gamma_\theta(\alpha) = \theta \circ \alpha$ , is commutative:

\begin{array}{ccc} H^k(\mathrm{Homgr}_A(N, E')) & \xrightarrow{H^{k+n}(\mathrm{Homgr}_A(1_N, \sigma))} & H^{k+n}(\mathrm{Homgr}_A(N, E)) \\ \downarrow \varphi^k(N, E') & & \downarrow \varphi^{k+n}(N, E) \\ \mathrm{Ext}_A^k(N, M') & \xrightarrow{\gamma_\theta} & \mathrm{Ext}_A^{k+n}(N, M) \end{array}

This is proved in a way analogous to Proposition 8.

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

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