# Definition:Small Category

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## 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

## Sources

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