List of dualities
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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
- Grothendieck local duality
- Hodge dual
- Isbell duality
- Jónsson–Tarski duality
- Lagrange duality
- Langlands dual
- Lefschetz duality
- Local Tate duality
- Opposite category
- Poincaré duality
- Poitou–Tate duality
- Pontryagin duality
- S-duality (homotopy theory)
- Schur–Weyl duality
- Series-parallel duality[1][2]
- Serre duality
- Spanier–Whitehead duality
- Stone's duality
- Tannaka–Krein duality
- Verdier duality
Philosophy and religion
Engineering
Physics
- Babinet's principle (electromagnetism)
- 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 (M-theory)
- Seiberg duality
- String duality
- Wave–particle duality