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Subobject classifier

In the mathematical field of category theory, a subobject classifier is a special object Ω {\displaystyle \Omega } of a category such that, informally, the subobjects of any object X {\displaystyle X} correspond to the morphisms from X {\displaystyle X} to Ω {\displaystyle \Omega } . This provides an analogue of the set of Booleans { 0 , 1 }…

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Subobject classifier

Nodes33
Edges32
Triples18
Avg. degree1.94
Density0.060606
Components1

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Subobject classifier

Top relations

related to Definition · 8
Subobject classifier → Equivalently, Let, Omega, Set, Sub, That, This, When
related to Sheaves of sets · 4
Subobject classifier → For, Given, Roughly, The
related to Elementary topoi · 3
Subobject classifier → Both, Grothendieck, The
is a · 2
Subobject classifier → object Ω, special object Ω
see also · 1
Subobject classifier → Quasitopos

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Important terminology

displaystyle category subobject classifier isbn set topos object elementary omega theory sets every press sheaves subobjects pullback springer-verlag mathcal morphism

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Subobject classifieris aspecial object Ω0.90text
Subobject classifieris aobject Ω0.90text
Subobject classifierrelated to DefinitionLet0.60section
Subobject classifierrelated to DefinitionOmega0.60section
Subobject classifierrelated to DefinitionThis0.60section
Subobject classifierrelated to DefinitionEquivalently0.60section
Subobject classifierrelated to DefinitionSub0.60section
Subobject classifierrelated to DefinitionSet0.60section
Subobject classifierrelated to DefinitionThat0.60section
Subobject classifierrelated to DefinitionWhen0.60section
Subobject classifierrelated to Elementary topoiBoth0.60section
Subobject classifierrelated to Elementary topoiThe0.60section

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