List of dualities

Mathematics
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
 * Artin–Verdier duality
 * Beta-dual space
 * Coherent duality
 * Conjugate hyperbola
 * 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
 * Hodge dual
 * Isbell duality
 * 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
 * Series-parallel duality
 * Serre duality
 * Spanier–Whitehead duality
 * Stone's duality
 * Tannaka–Krein duality
 * Verdier duality
 * Grothendieck local duality

Philosophy and religion

 * Dualism (philosophy of mind)
 * Epistemological dualism
 * Dualistic cosmology
 * Soul dualism
 * Yin and yang

Engineering

 * Duality (electrical circuits)
 * Duality (mechanical engineering)
 * Observability/Controllability in control theory

Physics

 * Complementarity (physics)
 * Dual resonance model
 * Duality (electricity and magnetism)
 * Englert–Greenberger duality relation
 * Holographic duality
 * Kramers–Wannier duality
 * Mirror symmetry
 * 3D mirror symmetry
 * Montonen–Olive duality
 * Mysterious duality (M-theory)
 * Seiberg duality
 * String duality
 * S-duality
 * T-duality
 * U-duality
 * Wave–particle duality

Economics and finance

 * Convex duality