In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...
24 KB (3,513 words) - 02:56, 11 August 2024
relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in...
63 KB (9,959 words) - 17:47, 25 September 2024
Limit (category theory) (redirect from Continuous functor)
like the strongly related notions of universal properties and adjoint functors, exist at a high level of abstraction. In order to understand them, it...
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up functor in Wiktionary, the free dictionary. A functor, in mathematics, is a map between categories. Functor may also refer to: Predicate functor in...
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Yoneda lemma (redirect from Yoneda functor)
is a fundamental result in category theory. It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation...
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a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle F:C\to...
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between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous applications in category...
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In functional programming, a functor is a design pattern inspired by the definition from category theory that allows one to apply a function to values...
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particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations...
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Natural transformation (category Functors)
mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition...
33 KB (5,663 words) - 12:43, 25 June 2024