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Duality (mathematics) In mathematics, a duality 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. Such involutions sometimes have fixed points, so that the dual ...
Dual diagnosis (also called co-occurring disorders ( COD) or dual pathology) [1] [2] is the condition of having a mental illness and a comorbid substance use disorder. There is considerable debate surrounding the appropriateness of using a single category for a heterogeneous group of individuals with complex needs and a varied range of problems ...
Six-wheel drive. Six-wheel drive ( 6WD or 6×6) is an all-wheel drive drivetrain configuration of three axles with at least two wheels on each axle capable of being driven simultaneously by the vehicle's engine. Unlike four-wheel drive drivetrains, the configuration is largely confined to heavy-duty off-road and military vehicles, such as all ...
Medicare dual eligible. Dual-eligible beneficiaries ( Medicare dual eligibles or "duals") refers to those qualifying for both Medicare and Medicaid benefits. In the United States, approximately 9.2 million people are eligible for "dual" status. [1] [2] Dual-eligibles make up 14% of Medicaid enrollment, yet they are responsible for approximately ...
Section (category theory) is a retraction of . is a section of . In category theory, a branch of mathematics, a section is a right inverse of some morphism. Dually, a retraction is a left inverse of some morphism . In other words, if and are morphisms whose composition is the identity morphism on , then is a section of , and is a retraction of .
In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities ...
Duality (order theory) 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 Pop or Pd. This dual order Pop is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P.
Dual (category theory) 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 Cop. 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 ...