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- Dual_(category_theory) abstract "For general notions of duality in mathematics, see duality (mathematics).In category theory, a branch of mathematics, duality is a correspondence between properties of a category C and so-called dual properties of the opposite category Cop. Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite category Cop. Duality, as such, is the assertion that truth is invariant under this operation on statements. In other words, if a statement is true about C, then its dual statement is true about Cop. Also, if a statement is false about C, then its dual has to be false about Cop.Given a concrete category C, it is often the case that the opposite category Cop per se is abstract. Cop need not be a category that arises from mathematical practice. In this case, another category D is also termed to be in duality with C if D and Cop are equivalent as categories. In the case when C and its opposite Cop are equivalent, such a category is self-dual.".
- Dual_(category_theory) wikiPageID "310885".
- Dual_(category_theory) wikiPageRevisionID "583873305".
- Dual_(category_theory) hasPhotoCollection Dual_(category_theory).
- Dual_(category_theory) id "p/d034090".
- Dual_(category_theory) id "p/d034120".
- Dual_(category_theory) id "p/d034130".
- Dual_(category_theory) title "Dual category".
- Dual_(category_theory) title "Duality principle".
- Dual_(category_theory) title "Duality".
- Dual_(category_theory) subject Category:Category_theory.
- Dual_(category_theory) subject Category:Duality_theories.
- Dual_(category_theory) type Abstraction100002137.
- Dual_(category_theory) type Cognition100023271.
- Dual_(category_theory) type DualityTheories.
- Dual_(category_theory) type Explanation105793000.
- Dual_(category_theory) type HigherCognitiveProcess105770664.
- Dual_(category_theory) type Process105701363.
- Dual_(category_theory) type PsychologicalFeature100023100.
- Dual_(category_theory) type Theory105989479.
- Dual_(category_theory) type Thinking105770926.
- Dual_(category_theory) comment "For general notions of duality in mathematics, see duality (mathematics).In category theory, a branch of mathematics, duality is a correspondence between properties of a category C and so-called dual properties of the opposite category Cop. Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite category Cop.".
- Dual_(category_theory) label "Dual (category theory)".
- Dual_(category_theory) label "Dual (teoría de categorías)".
- Dual_(category_theory) label "Duale (categorietheorie)".
- Dual_(category_theory) label "Двойственность (теория категорий)".
- Dual_(category_theory) sameAs Dual_(teoría_de_categorías).
- Dual_(category_theory) sameAs Duale_(categorietheorie).
- Dual_(category_theory) sameAs m.01t591.
- Dual_(category_theory) sameAs Q2361385.
- Dual_(category_theory) sameAs Q2361385.
- Dual_(category_theory) sameAs Dual_(category_theory).
- Dual_(category_theory) wasDerivedFrom Dual_(category_theory)?oldid=583873305.
- Dual_(category_theory) isPrimaryTopicOf Dual_(category_theory).