# Definition:Cartesian Closed Category

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## Definition

Let $\mathbf C$ be a metacategory.

Then $\mathbf C$ is called **Cartesian closed** if and only if $\mathbf C$ is a metacategory with finite products and with exponentials.

## Also known as

In more in-depth treatments of category theory, **Cartesian closed category** is often abbreviated to **CCC**.

## Also see

## Source of Name

This entry was named for RenĂ© Descartes.

## Sources

- 2010: Steve Awodey:
*Category Theory*(2nd ed.) ... (previous) ... (next): $\S 6.2$: Definition $6.2$