Adjoint Functor
- 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
- 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).