Proposition 6

Let $K, M, N$ be left $A$-modules, $P, Q, R$ right $A$-modules, $\alpha \in \mathrm{Ext}_A^n(P, Q)$, $\beta \in \mathrm{Ext}_A^p(Q, R)$, $\lambda \in \mathrm{Ext}_A^r(K, M)$, $\mu \in \mathrm{Ext}_A^s(M, N)$, $\gamma \in \mathrm{Tor}_m^A(P, K)$. Then (13)

(14) (15)

Formulas (13) and (14) follow immediately from the definitions. Let us prove (15). Let $z = \sum z_{ij}$, $z_{ij} \in L_i(P) \otimes L_j(K)$ be a cycle representing $\gamma$, $f : L(P) \to L(Q) (-n)$ and $g : L(K) \to L(M) (-r)$ morphisms representing $\alpha$ and $\lambda$. Then $\lambda \circ (\alpha \circ \gamma)$ is the class of $\sum (-1)^{(i-n)r} (f \otimes g)(z_{ij})$ and $\alpha \circ (\lambda \circ \gamma)$ is the class of