abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
2-natural transformation?
A dual adjunction between categories $C$ and $D$ is an adjunction between the opposite category $C^{op}$ of $C$ and $D$.
The concept arises in the context of duality.
Dual adjunctions between concrete categories may be represented by dualizing objects.
Dual adjunctions between posets are also called Galois connections.