\begin{definition}[Definition:Inclusion Relation on Subobject Classes]
Let $\mathbf C$ be a metacategory.
Let $C$ be an object of $\mathbf C$.
The '''inclusion relation $\subseteq$''' on subobject classes of $C$ is defined as follows:
:$\eqclass m {} \subseteq \eqclass {m'} {}$ {{iff}} there exists a morphism $\eqclass f {}: \eqclass m {} \to \eqclass {m'} {}$
\end{definition}