10.131.4.2

\begin{equation} \label{algebra-equation-map-presentations} \vcenter { \xymatrix{ \bigoplus S'[(a', b')] \oplus \bigoplus S'[(f', g')] \oplus \bigoplus S'[r'] \ar[r] & \bigoplus S' [a'] \\ \\ \bigoplus S[(a, b)] \oplus \bigoplus S[(f, g)] \oplus \bigoplus S[r] \ar[r] \ar[uu]^{ \begin{matrix} [(a, b)] \mapsto [(\varphi (a), \varphi (b))]
\\ [(f, g)] \mapsto [(\varphi (f), \varphi (g))]
\\ [r]\mapsto [\psi (r)]
\end{matrix} } & \bigoplus S[a] \ar[uu]_{[a] \mapsto [\varphi (a)]} } } \end{equation}

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