Definition:Small Category

Definition

Let $\mathbf C$ be a metacategory.

Then $\mathbf C$ is said to be small if and only if both of the following hold:

The collection of objects $\mathbf C_0$ is a set;

The collection of morphisms $\mathbf C_1$ is a set.

Also known as

In the index of Abelian Categories 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."

Also see

• Definition:Large Category

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (next): $\S 1.8$: Definition $1.11$