Editing Representable functor (section)

{{Short description|Functor type}}
In [[mathematics]], particularly [[category theory]], a '''representable functor''' is a certain [[functor]] from an arbitrary [[category (mathematics)|category]] into the [[category of sets]]. Such functors give representations of an abstract category in terms of known structures (i.e. [[Set (mathematics)|sets]] and [[function (mathematics)|function]]s) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings.

From another point of view, representable functors for a category ''C'' are the functors ''given'' with ''C''. Their theory is a vast generalisation of [[upper set]]s in [[poset]]s, and [[Yoneda lemma|Yoneda's representability]] theorem generalizes [[Cayley's theorem]] in [[group theory]].