Editing Natural transformation (section)

==Yoneda lemma==

{{Main|Yoneda lemma}}
If <math>X</math> is an object of a [[locally small category]] <math>C</math>, then the assignment <math>Y \mapsto \text{Hom}_{C}(X, Y)</math> defines a covariant functor <math>F_X: C \to \textbf{Set}</math>. This functor is called ''[[representable functor|representable]]'' (more generally, a representable functor is any functor naturally isomorphic to this functor for an appropriate choice of <math>X</math>). The natural transformations from a representable functor to an arbitrary functor <math>F: C \to \textbf{Set}</math> are completely known and easy to describe; this is the content of the [[Yoneda lemma]].