##  [Yoneda Lemma](/yoneda-lemma) 

  ##  [Yoneda Lemma](https://mathlogic.quantumdictionary.io/yoneda-lemma-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A statement in category theory that for any locally small category C, object A in C, and functor F: C^op → Set, there is a natural bijection between natural transformations Hom_C(-,A) ⇒ F and elements of the set F(A); this bijection is natural in both A and F and yields the Yoneda embedding of C into the functor category [C^op,Set].

 

 

 

 

 





 

 



 ##  [Yoneda Lemma](https://algebra.quantumdictionary.io/yoneda-lemma-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A fundamental result in category theory that identifies the elements of a presheaf at an object with natural transformations from the representable functor Hom(−, A) to that presheaf, thereby representing objects of a category by their functors of points and establishing a fully faithful embedding of the category into a presheaf category.