 ##  [Adjunction](/index.php/adjunction) 

  ##  [Adjunction](https://natural.quantumdictionary.io/adjunction-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/index.php/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

A datum of a pair of functors L : C → D and R : D → C together with, for each X in C and Y in D, a natural bijection Hom_D(L(X),Y) ≅ Hom_C(X,R(Y)) that is natural in X and Y. Equivalently specified by unit and counit natural transformations satisfying triangle identities. It encodes a universal best‑approximation relationship: L is left adjoint to R and R right adjoint to L.

 
 ##  [Adjunction](https://puremath.quantumdictionary.io/adjunction-1) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A relationship between two functors L : C → D and R : D → C given by a natural bijection Hom_D(L(X), Y) ≅ Hom_C(X, R(Y)) natural in X∈C and Y∈D, equivalently specified by a unit η: Id_C ⇒ R∘L and counit ε: L∘R ⇒ Id_D satisfying the triangle identities.