In mathematics, a **duality**, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of *A* is *B*, then the dual of *B* is *A*.

Alexander duality
Alvis–Curtis duality
Araki duality
Beta-dual space
Coherent duality
De Groot dual
Dual abelian variety
Dual basis in a field extension
Dual bundle
Dual curve
Dual (category theory)
Dual graph
Dual group
Dual object
Dual pair
Dual polygon
Dual polyhedron
Dual problem
Dual representation
Dual q-Hahn polynomials
Dual q-Krawtchouk polynomials
Dual space
Dual topology
Dual wavelet
Duality (optimization)
Duality (order theory)
Duality of stereotype spaces
Duality (projective geometry)
Duality theory for distributive lattices
Dualizing complex
Dualizing sheaf
Eckmann–Hilton duality
Esakia duality
Fenchel's duality theorem
Haag duality
Hodge dual
Jónsson–Tarski duality
Lagrange duality
Langlands dual
Lefschetz duality
Local Tate duality
Opposite category
Poincaré duality
Twisted Poincaré duality
Poitou–Tate duality
Pontryagin duality
S-duality (homotopy theory)
Schur–Weyl duality
Serre duality
Spanier–Whitehead duality
Stone's duality
Tannaka–Krein duality
Verdier duality
Dualism (philosophy of mind)
Yin and yang
Duality (electrical circuits)
Duality (mechanical engineering)
Complementarity (physics)
Dual resonance model
Duality (electricity and magnetism)
Englert–Greenberger duality relation
Holographic duality
Kramers–Wannier duality
Mirror symmetry
Montonen–Olive duality
Mysterious duality
String duality
S-duality
T-duality
U-duality
Wave-particle duality