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Representable functor

In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings.

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Definition

Universal elements

Examples

Properties

Relation to universal morphisms and adjoints

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Representable functor

Nodes60
Edges59
Triples15
Avg. degree1.97
Density0.033333
Components1

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Representable functor

Top relations

related to Relation to universal morphisms and adjoints · 8
Representable functor → FX, HomC, HomD, It, Let, Set, The, Then
related to Preservation of limits · 5
Representable functor → Contravariant, Hom, In, It, Representable
is a · 1
Representable functor → certain functor from an arbitrary category into the category of sets

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Important terminology

functor set category representable displaystyle represented functors hom universal object sets natural function unique isomorphism element may forgetful space elements

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Representable functoris acertain functor from an arbitrary category into the category of sets0.90text
stacksinstance ofnon-representable functors may be described by more complicated structures0.80text
Representable functorrelated to Preservation of limitsRepresentable0.60section
Representable functorrelated to Preservation of limitsHom0.60section
Representable functorrelated to Preservation of limitsIn0.60section
Representable functorrelated to Preservation of limitsIt0.60section
Representable functorrelated to Preservation of limitsContravariant0.60section
Representable functorrelated to Relation to universal morphisms and adjointsThe0.60section
Representable functorrelated to Relation to universal morphisms and adjointsLet0.60section
Representable functorrelated to Relation to universal morphisms and adjointsThen0.60section
Representable functorrelated to Relation to universal morphisms and adjointsHomC0.60section
Representable functorrelated to Relation to universal morphisms and adjointsSet0.60section

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