Product category

In the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is a straightforward extension of the concept of the Cartesian product of two sets.

Definition

The product category C × D has:

Relation to other categorical concepts

For small categories, this is the same as the action on objects of the categorical product in the category Cat. A functor whose domain is a product category is known as a bifunctor. An important example is the Hom functor, which has the product of the opposite of some category with the original category as domain: