A dual adjunction consists of contravariant functors , together with natural transformations and such that and .
Reformulated in terms of covariant functors, a dual adjunction can be viewed as an ordinary adjunction with and , or as with and . However, it is often useful not to break the symmetry of the contravariant formulation.
A self-dual adjunction is a dual adjunction for which and . An example is where is a symmetric monoidal closed category and is an internal hom into an object , where the unit is the usual double-dual embedding .
Revised on January 25, 2015 19:00:20
by Todd Trimble