Definition:Locally Small Category

Definition
Let $\mathbf C$ be a metacategory.

Then $\mathbf C$ is said to be locally small all of its hom classes are sets.

That is, 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.