nLab duality - contents

duality

• abstract duality: opposite category,

  Eckmann-Hilton duality

• concrete duality: dual object, dualizable object, fully dualizable object, dualizing object

  • dual vector space

Examples

• between higher geometry/higher algebra

  • Isbell duality

  • Stone duality

  • Gelfand duality

• Tannaka duality

• Langlands duality, geometric Langlands duality, quantum geometric Langlands duality

• Pontryagin duality

  • Cartier duality

• Poincaré duality for manifolds

• Koszul duality

• Spanier-Whitehead duality

• Grothendieck duality

In QFT and String theory

duality in physics, duality in string theory

• Seiberg duality, AGT conjecture

• S-duality

  • electro-magnetic duality, Montonen-Olive duality, geometric Langlands duality

• T-duality

  • mirror symmetry

• U-duality

• open/closed string duality

  • AdS/CFT duality

  • KLT relations