Corollary 2

If $\theta \in \mathrm{Ext}_A^n(M, N)$ is the class associated with the exact sequence $(\mathscr{S})$, we have $\hat{\partial}_m(P, \mathscr{S})(\alpha) = \theta \circ \alpha$ for all $\alpha \in \mathrm{Tor}_m^A(P, M)$.