Functor Category

Functor Category

In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms are natural transformations between the functors. Functor categories are of interest for two main reasons:

• many commonly occurring categories are (disguised) functor categories, so any statement proved for general functor categories is widely applicable;
• every category embeds in a functor category (via the Yoneda embedding); the functor category often has nicer properties than the original category, allowing certain operations that were not available in the original setting.