Definition:Small Category

Definition
Let $\mathcal C$ be a category.

If $\mathcal C$ is a set then $\mathcal C$ is small.

If for any two objects of $\mathcal C$, the Hom class $\operatorname{Hom}(X,Y)$ is a set, then $\mathcal C$ is locally small.

Alternative Name
In the index of by Peter Freyd there is an entry Kittygory.

On checking back in the book to see what it refers to, you find:
 * "If $\mathscr M$ is a set we shall call it a small category."