List of dualities

This article is about a listing of dualities in mathematics, philosophy and science. For other uses, see Duality (disambiguation).

Mathematics

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^[1][2]
• 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
  • AdS/CFT correspondence
• 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^[1][2]

See also

• Mechanical–electrical analogies

References

1. Ellerman, David Patterson (1995-03-21). "Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics". Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics (PDF). G - Reference, Information and Interdisciplinary Subjects Series (illustrated ed.). Rowman & Littlefield Publishers, Inc. pp. 237–268. ISBN 0-8476-7932-2. Archived (PDF) from the original on 2016-03-05. Retrieved 2019-08-09. […] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the series sum) of the resistances a + b. If the resistances are placed in parallel, their compound resistance is the parallel sum of the resistances, which is denoted by the full colon […] {{cite book}}: |work= ignored (help) (271 pages)
2. Ellerman, David Patterson (May 2004) [1995-03-21]. Introduction to Series-Parallel Duality (PDF). University of California at Riverside. CiteSeerX 10.1.1.90.3666. Archived from the original on 2019-08-10. Retrieved 2019-08-09. The parallel sum of two positive real numbers x:y = [(1/x) + (1/y)]⁻¹ arises in electrical circuit theory as the resistance resulting from hooking two resistances x and y in parallel. There is a duality between the usual (series) sum and the parallel sum. […] (24 pages)