physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
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
In fundamental physics, notably in quantum field theory and string theory one often says that a non-trivial equivalence between two models (in theoretical physics) is a duality.
While most of these dualities refer to equivalences between quantum field theories, they find their conceptual explanation in string theory. See at
for more.
In some cases such as Montonen-Olive duality/S-duality the equivalence involves some actual duality in the mathematical sense, as in replacing the gauge group by its Langlands dual group. In T-duality only simple cases exhibit such obviously “dual” behaviour and in general cases such as U-duality really only the notion of equivalence remains.
There is also a duality in the description of physics:
duality between algebra and geometry in physics: