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Functor

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces. Nowadays, functors are used…

Examples, Definition & Relation to other categorical concepts

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Computer implementations

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Map overview Semantic statistics

Functor

Nodes102
Edges101
Triples57
Avg. degree1.98
Density0.019608
Components1

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Functor

Top relations

related to External links · 31
Functor → Abstract, Adamek, An, André Joyal, Archived, Categorical Primer, Category Theory, CatLab, Cats Archived, Chris, Concrete Categories-The Joy, EMS Press, Encyclopedia, Extensive, Herrlich, Interactive Web, Jean-Pierre Marquis, John, List, Manipulation
related to Bifunctors and multifunctors · 5
Functor → For, Hom, It, Set, So
related to Opposite functor · 5
Functor → By, Every, For, Note, Since
related to Computer implementations · 4
Functor → For, Functors, Hask, Haskell
related to Relation to other categorical concepts · 4
Functor → Functors, Let, Morphisms, The
is a · 2
Functor → endofunctor, mapping between categories
related to Covariance and contravariance · 2
Functor → There, We
see also · 2
Functor → AnafunctorProfunctorFunctor, Mathematics
related to Definition · 1
Functor → Let
related to Properties · 1
Functor → Two

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Important terminology

displaystyle functors category categories morphisms mathrm mathematics contravariant theory op object composition also circ one every covariant used opposite see

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Functoris amapping between categories0.90text
Functoris aendofunctor0.90text
Functorrelated to Bifunctors and multifunctorsFor0.60section
Functorrelated to Bifunctors and multifunctorsHom0.60section
Functorrelated to Bifunctors and multifunctorsSet0.60section
Functorrelated to Bifunctors and multifunctorsIt0.60section
Functorrelated to Bifunctors and multifunctorsSo0.60section
Functorrelated to Computer implementationsFunctors0.60section
Functorrelated to Computer implementationsFor0.60section
Functorrelated to Computer implementationsHaskell0.60section
Functorrelated to Computer implementationsHask0.60section
Functorrelated to Covariance and contravarianceThere0.60section

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    Min side: 3
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