\begin{definition}[Definition:Hom Class]
Let $\mathbf C$ be a metacategory.
Let $C$ and $D$ be objects of $\mathbf C$.
The collection of morphisms $f: C \to D$ is called a '''hom class''' and is denoted $\operatorname{Hom}_{\mathbf C} \left({C, D}\right)$.
\end{definition}