This is an excerpt from Homework Sheet 4. It uses the package Xy-pic. For more information, please check the Xy-pic User's Guide.

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Here are some examples of graphical representations of these operations:

\noindent
$\mathsf{s}_3$:
\xymatrix@R=5mm@C=13mm{
\mbox{ AaB }&  & \mbox{ AaB }\\
\mbox{ BiC }& & \mbox{ BiC }\\\hline
\overline{\mbox{ CiA }}\ar[rr]^{\mathsf{s}} & & \overline{\mbox{ AiC }}
}
\hspace{4mm}
$\mathsf{p}_1$:
\xymatrix@R=5mm@C=13mm{
\mbox{ AiB }\ar[rr]^{\mathsf{p}}& & \mbox{ AaB }\\
\mbox{ AaB }& & \mbox{ AaB }\\\hline
\overline{\mbox{ AaC }}        & & \overline{\mbox{ AaC }}
}
\hspace{4mm}
$\mathsf{m}$:
\xymatrix@R=5mm@C=13mm{
\mbox{ AaB }\ar[rrd]^{\mathsf{m}}&  & \mbox{ CaB }\\
\mbox{ CaB }\ar[rru]& & \mbox{ AaB }\\\hline
\overline{\mbox{ AaC }}        & & \overline{\mbox{ AaC }}
}\\[3mm]

\noindent
$\mathsf{c}_1$:
\xymatrix@R=5mm@C=13mm{
\mbox{ AoB }\ar[rrdd]^{\mathsf{c}}&  & \mbox{ AaC }\\
\mbox{ CaB }         & & \mbox{ CaB }\\\hline
\overline{\mbox{ AoC }}\ar[rruu]        & & \overline{\mbox{ AaB }}
}
\hspace{4mm}
$\mathsf{per}$:
\xymatrix@R=5mm@C=13mm{
\mbox{ BaA }&  & \mbox{ AaB }\\
\mbox{ AaC }\ar@/^1pc/[rr]^{\mathsf{per}}& & \mbox{ BaC }\\\hline
\overline{\mbox{ BaC }}        & & \overline{\mbox{ AaC }}
}
\end{document}