ProphetesAI is thinking...
functor
MindMap
Loading...
Sources
Functor - Wikipedia
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology.
en.wikipedia.org
en.wikipedia.org
Functor (functional programming) - Wikipedia
A functor is a design pattern inspired by the definition from category theory that allows one to apply a function to values inside a generic type
en.wikipedia.org
en.wikipedia.org
Functors (Function Objects)
A functor, also known as a function object, is an object that is able to be called as if it were a function.
www.cs.fsu.edu
www.cs.fsu.edu
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
prophetes.ai
Functors in C++ - GeeksforGeeks
Functors are objects that can be treated as though they are a function or function pointer. Functors are most commonly used along with STLs.
www.geeksforgeeks.org
www.geeksforgeeks.org
category theory - The definition of functor. Is a functor a function?
A (covariant) functor F:C→D of categories sends objects of C to those of D, and similarly morphisms in C to morphisms of D, such that the following three hold ...
math.stackexchange.com
math.stackexchange.com
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 ...
wiki.haskell.org
Functor - Typelevel
Functor is a type class that abstracts over type constructors that can be map 'ed over. Examples of such type constructors are List, Option, and Future.
typelevel.org
typelevel.org
What are C++ functors and their uses? - Stack Overflow
A functor is pretty much just a class which defines the operator(). That lets you create objects which look like a function.
stackoverflow.com
stackoverflow.com
Functor - HaskellWiki - Haskell.org
The Functor typeclass represents the mathematical functor: a mapping between categories in the context of category theory.
www.haskell.org
www.haskell.org
functor in nLab
A functor maps not hom-sets but the given hom-objects to each other, in a way that respects their composition.
ncatlab.org
ncatlab.org
Understanding functors, morphisms and functions : r/CategoryTheory
Functors, morphisms and functions are all mappings between objects. They can be composed, and such composition is associative but not commutative.
www.reddit.com
www.reddit.com
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
en.wikipedia.org
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 ...
mathworld.wolfram.com
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.
math.stackexchange.com