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.