\begin{definition}[Definition:Locally Small Category]
Let $\mathbf C$ be a metacategory.
Then $\mathbf C$ is said to be '''locally small''' {{iff}} all of its hom classes are sets.
That is, {{iff}} for all objects $X, Y \in \mathbf C_0$ of $\mathbf C$:
:$\operatorname{Hom}_{\mathbf C} \left({X, Y}\right) = \set {f \in \mathbf C_1: f: X \to Y}$
is a set.
\end{definition}