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functor
functor (ˈfʌŋktə(r)) [f. function n. + -or, after type factor.] 1. Logic. A function or operator.1937 A. Smeaton tr. Carnap's Logical Syntax Lang. §3. p. 14 In order to express properties or relations of position by means of numbers, we shall use functors. Ibid., Besides such descriptive functors, w... Oxford English Dictionary
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Functor - HaskellWiki
Description. An abstract datatype f a, which has the ability for its value (s) to be mapped over, can become an instance of the Functor typeclass. That is to say, a new Functor, f b, can be made from f a by transforming all of its value (s), whilst leaving the structure of f itself unmodified. Declaring f an instance of Functor allows functions ...
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Group functor
In mathematics, a group functor is a group-valued functor on the category of commutative rings. Group functor as a generalization of a group scheme A scheme may be thought of as a contravariant functor from the category of S-schemes to the category wikipedia.org
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Exact Functor -- from Wolfram MathWorld
Jan 23, 2024and it is called right exact if it preserves the exactness of all sequences ("Left" and "right" are interchanged in the corresponding definitions for contravariant functors.). A functor is exact iff it is both left and right exact.. Every tensor product functor is right exact. For every module over a unit ring, the covariant functor and the contravariant functor are left exact; the first is ...
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Is an exact functor half exact? - Mathematics Stack Exchange
Closed 2 years ago. I am working with R -modules, where R i a commutative ring. If F is an additive covariant exact functor between R M o d and S M o d, is the following proposition true? I like references. M → N → L is exact ⇒ F M → F N → F L is exact. *For me, exact functors preserve short exact sequences. abstract-algebra.
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Zuckerman functor
The Bernstein functor is closely related. Definition The Zuckerman functor Γ is defined by and the Bernstein functor Π is defined by References David A. wikipedia.org
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Exact functor - Wikipedia
Exact functor. In mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations because they can be directly applied to presentations of objects.
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Dominant functor
In category theory, an abstract branch of mathematics, a dominant functor is a functor F : C → D in which every object of D is a retract of an object of wikipedia.org
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Monoidal functor
Variants The dual of a monoidal functor is a comonoidal functor; it is a monoidal functor whose coherence maps are reversed. A strict monoidal functor is a monoidal functor whose coherence maps are identities. wikipedia.org
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Fiber functor
In category theory, a branch of mathematics, a fiber functor is a faithful k-linear tensor functor from a tensor category to the category of finite-dimensional Definition A fiber functor (or fibre functor) is a loose concept which has multiple definitions depending on the formalism considered. wikipedia.org
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Functor and Applicative Functor Usage in TypeScript - Semantic Scholar
T theoretical explanations of the Functor and Applicative Functor concepts in category theory are presented and their implementations in TypeScript are provided, focusing on Maybe and List functors. : Leveraging functional programming concepts to make front-end application development faster and easier, with fewer bugs has been tried with pure functional programming languages such as Elm.
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[Functional Programming] Async IO Functor - 编程猎人
'localStorage' is a side effect, but we wrap into a function call, so what 'getFromStorage' return is not a value but a function. And this returned function is waiting to be called, before calling, we can do all kind of function mapping of composion on it, that's the beautity.
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Conservative functor
In category theory, a branch of mathematics, a conservative functor is a functor such that for any morphism f in C, F(f) being an isomorphism implies More generally, every monadic functor is conservative. wikipedia.org
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函数式编程里functor到底该怎么理解？ - 知乎
带type system的函数式编程的核心就是 （数学）结构 。. 也就是说，你的程序是不同结构之间的互动，你如果理解了这一点，函数式编程里的所有概念都会很容易理解。. 比方说，你可以实现一个加一的函数. (1+) 那么你传入任何整数都会加上1。. 那么如果你有一个 ...
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Signalizer functor
The signalizer functor theorem gives conditions under which a signalizer functor comes from a subgroup. W) is normal in References Signalizer functor wikipedia.org
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