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\begin{definition}
A concrete \emph{metagraph} $\mathcal{M}_G$ consists of objects, $A, B, C,$...
and arrows $f, g, h,$... between objects, and two operations as follows:
\begin{itemize}
\item a {\em Domain operation}, $dom$, which assigns to each arrow $f$ an object $A~ =~dom ~f$
\item a {\em Codomain operation}, $cod$, which assigns to each arrow $f$ an object $B~ = ~cod ~f,$
represented as $f: A \to B$ or $A \stackrel{f}{\longrightarrow} B$
\end{itemize}
\end{definition}
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