Definition. Product category [dm-000N]

For two categories \textbf {A} and \textbf {B}, the product category \textbf {A} \times \textbf {B} is the category whose objects are pairs consisting of an object of \textbf {A} and an object of \textbf {B}, and whose morphisms are similarly pairs of morphisms from \textbf {A} and \textbf {B}. Composition of morphisms is defined componentwise on the pairs using the composition from \textbf {A} and \textbf {B}.