Proposition 2

We have $a, b \in Z^n(\mathrm{Homgr}_A(L(M), I(N)))$. Moreover, the classes $\overline{a}$ and $\overline{b}$ of $a$ and $b$ in $H^n(\mathrm{Homgr}_A(L(M), I(N))) = \mathrm{Ext}_A^n(M, N)$ depend only on the exact sequence (4) and are equal.

By prop. 1, applied to the two extreme rows of (5) and to the composed vertical arrows, with $p = n, q = 0$, we have $a, b \in Z^n(\mathrm{Homgr}_A(I(M), L(N)))$ and

Since $a$ (resp. $b$) is independent of the choice of $u$ (resp. $v$), the element $\overline{a} = \overline{b}$ of $\mathrm{Ext}_A^n(M, N)$ is independent of the choice of the morphisms $u$ and $v$, whence the proposition.