Definition:Locally Small Category

Definition
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 $\mathbf C$:


 * $\operatorname{Hom}_{\mathbf C} \left({X, Y}\right) = \left\{{f \in \mathbf C_1 }\ \middle\vert \ {f: X \to Y}\right\}$

is a set.