\begin{definition}[Definition:Equivalent Subobjects]
Let $\mathbf C$ be a metacategory.
Let $C$ be an object of $\mathbf C$.
Let $\map {\mathbf{Sub}_{\mathbf C} } C$ be the category of subobjects of $C$.
Two subobjects $m, m'$ of $C$ are said to be '''equivalent''' {{iff}}:
:$m \subseteq m'$ and $m' \subseteq m$
where $\subseteq$ denotes the inclusion relation on subobjects.
\end{definition}