Definition:Hom Class

Definition
Let $\mathcal C$ be a category.

The hom-classes of $\mathcal C$ are the classes $\operatorname{Hom}_{\mathcal C}(X,Y)$ of morphisms $X \to Y$ for any two objects $X, Y \in \mathcal C_0$.

If $\operatorname{Hom}(X,Y)$ is a set, then it is also called a hom-set