List of dualities explained

Mathematics

See main article: Duality (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

See also: Dualism (disambiguation).

• 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

See also

• Mechanical–electrical analogies