Product category

In the mathematical field of category theory, the product of two categories "C" and "D", denoted and called a product category, is an extension of the concept of the Cartesian product of two sets. Product categories are used to define bifunctors and multifunctors.
Definition.
The product category 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:
Generalization to several arguments.
Just as the binary Cartesian product is readily generalized to an "n"-ary Cartesian product, binary product of two categories can be generalized, completely analogously, to a product of "n" categories. The product operation on categories is commutative and associative, up to isomorphism, and so this generalization brings nothing new from a theoretical point of view.