Subobject
Subobject In category theory, there is a general definition of subobject extending the idea of subset and subgroup ... a preorder, but the definition of a subobject ensures that the collection of subobjects of ... discussion given is somewhat loose. If the subobject-collection of every object is a set ... well-powered.) The dual concept to a subobject is a quotient object; that is, ...
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Subobject classifier
Subobject classifier In category theory, a subobject classifier is a special object Ω of ... the set Ω = {0,1} is a subobject classifier in the category of sets and ... The object Ω of C is a subobject classifier for C if there exists a ... then called the classifying morphism for the subobject j. Further examples Every topos has ...
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Talk:Subobject classifier
Talk:Subobject classifier What is the map 1 -> Ω ... intuitively represents the "true" point in the subobject classifier [StefanLjungstrand 84.217.41.47 20 ... examples (at the very least, the 'classical' subobject classifier in Set, and maybe one nonclassical ...
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Talk:Topos
... morphisms between an object S and the subobject classifier. I don't know of a ... definition that doesn't refer to the subobject classifier.--SurrealWarrior 20:44, 22 January 2006 ...
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List of mathematics articles (S)
... Submatrix -- Submersion -- Submodel -- Submodular function -- Subnormal subgroup -- Subobject -- Subobject classifier -- Subquadratic time -- Subquotient -- Subring -- Subsemigroup -- Subsequence ...
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Categorical logic
... Hegelian sense, not without some justification). A subobject classifier is a strong property to ask ... attributes, which in a sense is a subobject theory more in sympathy with type theory ...
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List of category theory topics
... Objects Initial object Terminal object Zero object Subobject Group object Magma object Natural number object ... theory) Grothendieck topology Introduction to topos theory Subobject classifier Pointless topology Heyting algebra See also ...
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List of mathematics articles (S-U)
... Submatrix -- Submersion -- Submodel -- Submodular function -- Subnormal subgroup -- Subobject -- Subobject classifier -- Subquadratic time -- Subquotient -- Subring -- Subsemigroup -- Subsequence ...
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Talk:Sheaf (mathematics)
... V when mean that V is a "subobject" of U in the fixed topology (I am abusing subobject a bit I know .. I mean that ...
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Topos
... index categories exist. The category has a subobject classifier. Any two objects have an exponential ... In many applications, the role of the subobject classifier is pivotal, whereas power objects are ...
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