abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
Examples
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
In QFT and String theory
Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
A dual adjunction between categories and is an adjunction between the opposite category of and .
The concept arises in the context of duality.
Dual adjunctions between concrete categories are frequently represented by dualizing objects.
Dual adjunctions between posets are also called Galois connections.
A dual adjunction consists of contravariant functors , together with natural transformations and such that and . In diagrams, the following must commute.
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 .
Last revised on October 6, 2021 at 11:50:16. See the history of this page for a list of all contributions to it.