Product of Categories and Product of Two Objects in a Category

Let  and  be categories. The product of two categories  and , is represented by  and referred to as the product category. Product category is an extension of the concept of the product of two sets of cartesian and is used to define the bifungtors. In the theory of categories there are also product of two objects in a category where the objects of the product itself is part of the category. The objects  in  is said to be a product of  and  in  if to each object  and to each pair  of morphisms with  and , there is an exactly morphism , such that  and . This article discusses the product categories and the product of two objects in a category, including concepts and properties related to the product of categories and the product of two objects in a category.