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Dual (category theory), a formalization of mathematical duality; Duality (optimization) Duality (order theory), a concept regarding binary relations; Duality (projective geometry), general principle of projective geometry; Duality principle (Boolean algebra), the extension of order-theoretic duality to Boolean algebras; S-duality (homotopy theory)
Dually may refer to: Dualla, County Tipperary, a village in Ireland; A pickup truck with dual wheels on the rear axle; DUALLy, s platform for architectural languages ...
A set C (blue) and its dual cone C * (red).. A duality in geometry is provided by the dual cone construction. Given a set of points in the plane (or more generally points in ), the dual cone is defined as the set consisting of those points (,) satisfying + for all points (,) in , as illustrated in the diagram.
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by P op or P d.This dual order P op is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in P op if and only if y ≤ x holds in P.
Adding the dually setup increases the price by several thousand dollars. The High-Output Cummins engine is a $12,595 option. Adding these options to a Limited Mega Cab will bring the price to more ...
A "dually" is a North American colloquial term for a pickup with four rear wheels instead of two, able to carry more weight over the rear axle. Vehicles similar to the pickup include the coupé utility, a car-based pickup, and the larger sport utility truck (SUT), based on a sport utility vehicle (SUV).
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category C op.Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite ...
For instance, we say that the categories C and D are equivalent (respectively dually equivalent) if there exists an equivalence (respectively duality) between them. Furthermore, we say that F "is" an equivalence of categories if an inverse functor G and natural isomorphisms as above exist.