Definition:Cartesian Closed Category

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

• Definition:Category with Finite Products
• Definition:Category with Exponentials

Source of Name

This entry was named for René Descartes.

Sources

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