Functors | Categories in category theory

Functor category

In category theory, a branch of mathematics, a functor category is a category where the objects are the functors and the morphisms are natural transformations between the functors (here, is another object in the category). 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. (Wikipedia).

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Related pages

Complete category | Category of sets | Group representation | Category of abelian groups | Vector space | Presheaf (category theory) | Discrete category | Group (mathematics) | Topos | Preadditive category | Exponential object | Product (category theory) | Natural transformation | Adjoint functors | Graph theory | Abelian category | Diagram (category theory) | Mathematics | Field (mathematics) | Sheaf (mathematics) | Yoneda lemma | Representable functor | Category theory | Ring (mathematics) | Morphism | Functor | Cartesian closed category | Grothendieck topology | Abelian group | Module (mathematics)