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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) wikiPageLength "4679".
- Dual_(category_theory) wikiPageOutDegree "32".
- Dual_(category_theory) wikiPageRevisionID "639334777".
- Dual_(category_theory) wikiPageWikiLink Algebraic_topology.
- Dual_(category_theory) wikiPageWikiLink Category:Category_theory.
- Dual_(category_theory) wikiPageWikiLink Category:Duality_theories.
- Dual_(category_theory) wikiPageWikiLink Category_theory.
- Dual_(category_theory) wikiPageWikiLink Codomain.
- Dual_(category_theory) wikiPageWikiLink Cofibration.
- Dual_(category_theory) wikiPageWikiLink Concrete_category.
- Dual_(category_theory) wikiPageWikiLink De_Morgans_laws.
- Dual_(category_theory) wikiPageWikiLink Domain_of_a_function.
- Dual_(category_theory) wikiPageWikiLink Dual_object.
- Dual_(category_theory) wikiPageWikiLink Duality_(mathematics).
- Dual_(category_theory) wikiPageWikiLink Duality_(order_theory).
- Dual_(category_theory) wikiPageWikiLink Eckmann–Hilton_duality.
- Dual_(category_theory) wikiPageWikiLink Epimorphism.
- Dual_(category_theory) wikiPageWikiLink Equivalence_of_categories.
- Dual_(category_theory) wikiPageWikiLink Fibration.
- Dual_(category_theory) wikiPageWikiLink First-order_logic.
- Dual_(category_theory) wikiPageWikiLink First_order_language.
- Dual_(category_theory) wikiPageWikiLink Function_composition.
- Dual_(category_theory) wikiPageWikiLink Homotopy.
- Dual_(category_theory) wikiPageWikiLink Homotopy_theory.
- Dual_(category_theory) wikiPageWikiLink Lattice_(order).
- Dual_(category_theory) wikiPageWikiLink Lattice_theory.
- Dual_(category_theory) wikiPageWikiLink Limit_(category_theory).
- Dual_(category_theory) wikiPageWikiLink Mathematics.
- Dual_(category_theory) wikiPageWikiLink Monomorphism.
- Dual_(category_theory) wikiPageWikiLink Morphism.
- Dual_(category_theory) wikiPageWikiLink Opposite_category.
- Dual_(category_theory) wikiPageWikiLink Partial_order.
- Dual_(category_theory) wikiPageWikiLink Partially_ordered_set.
- Dual_(category_theory) wikiPageWikiLink Set_(mathematics).
- Dual_(category_theory) wikiPageWikiLinkText "''dual'' or ''opposite category''".
- Dual_(category_theory) wikiPageWikiLinkText "Dual (category theory)".
- Dual_(category_theory) wikiPageWikiLinkText "Dual".
- Dual_(category_theory) wikiPageWikiLinkText "Duality".
- Dual_(category_theory) wikiPageWikiLinkText "Dually".
- Dual_(category_theory) wikiPageWikiLinkText "categorical dual".
- Dual_(category_theory) wikiPageWikiLinkText "dual (category theory)".
- Dual_(category_theory) wikiPageWikiLinkText "dual category".
- Dual_(category_theory) wikiPageWikiLinkText "dual notion".
- Dual_(category_theory) wikiPageWikiLinkText "dual notions".
- Dual_(category_theory) wikiPageWikiLinkText "dual".
- Dual_(category_theory) wikiPageWikiLinkText "opposite (or dual)".
- Dual_(category_theory) wikiPageWikiLinkText "opposite category".
- Dual_(category_theory) wikiPageWikiLinkText "opposite".
- Dual_(category_theory) wikiPageWikiLinkText "opposites".
- Dual_(category_theory) wikiPageWikiLinkText "self-dual".
- 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) wikiPageUsesTemplate Template:Reflist.
- Dual_(category_theory) wikiPageUsesTemplate Template:Springer.
- Dual_(category_theory) subject Category:Category_theory.
- Dual_(category_theory) subject Category:Duality_theories.
- 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) sameAs Dual_(teoría_de_categorías).
- Dual_(category_theory) sameAs Duale_(categorietheorie).
- Dual_(category_theory) sameAs m.01t591.
- Dual_(category_theory) sameAs Двойственность_(теория_категорий).
- Dual_(category_theory) sameAs Двоїста_категорія.
- Dual_(category_theory) sameAs Q2361385.
- Dual_(category_theory) sameAs Q2361385.
- Dual_(category_theory) wasDerivedFrom Dual_(category_theory)?oldid=639334777.
- Dual_(category_theory) isPrimaryTopicOf Dual_(category_theory).