##  [Adjoint Functor](/adjoint-functor) 

  ##  [Adjoint Functor](https://mathlogic.quantumdictionary.io/adjoint-functor-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 pair of functors L: C -> D and R: D -> C such that there is a natural bijection Hom_D(Lc, d) ≅ Hom_C(c, Rd) for all objects c in C and d in D; L is left adjoint to R and R is right adjoint to L.

 

 

 

 

 





 

 



 ##  [Adjoint Functor](https://algebra.quantumdictionary.io/adjoint-functor-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 pair of functors L: C → D and R: D → C equipped with a family of natural bijections Hom_D(L(c), d) ≅ Hom_C(c, R(d)) for all objects c in C and d in D, expressing a universal correspondence between maps out of L(c) and maps into R(d).