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- Browns_representability_theorem abstract "In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable functor.More specifically, we are givenF: Hotcop → Set,and there are certain obviously necessary conditions for F to be of type Hom(—, C), with C a pointed connected CW-complex that can be deduced from category theory alone. The statement of the substantive part of the theorem is that these necessary conditions are then sufficient. For technical reasons, the theorem is often stated for functors to the category of pointed sets; in other words the sets are also given a base point.".
- Browns_representability_theorem wikiPageID "1073746".
- Browns_representability_theorem wikiPageLength "6644".
- Browns_representability_theorem wikiPageOutDegree "32".
- Browns_representability_theorem wikiPageRevisionID "645943484".
- Browns_representability_theorem wikiPageWikiLink Adjoint_functor.
- Browns_representability_theorem wikiPageWikiLink Adjoint_functors.
- Browns_representability_theorem wikiPageWikiLink CW_complex.
- Browns_representability_theorem wikiPageWikiLink Category:Category_theory.
- Browns_representability_theorem wikiPageWikiLink Category:Homotopy_theory.
- Browns_representability_theorem wikiPageWikiLink Category:Representable_functors.
- Browns_representability_theorem wikiPageWikiLink Category:Theorems_in_algebraic_topology.
- Browns_representability_theorem wikiPageWikiLink Category_of_sets.
- Browns_representability_theorem wikiPageWikiLink Category_theory.
- Browns_representability_theorem wikiPageWikiLink Contravariant_functor.
- Browns_representability_theorem wikiPageWikiLink Coproduct.
- Browns_representability_theorem wikiPageWikiLink Coproducts.
- Browns_representability_theorem wikiPageWikiLink Derived_category.
- Browns_representability_theorem wikiPageWikiLink Eilenberg-MacLane_space.
- Browns_representability_theorem wikiPageWikiLink Eilenberg–MacLane_space.
- Browns_representability_theorem wikiPageWikiLink Functor.
- Browns_representability_theorem wikiPageWikiLink Grothendieck_duality.
- Browns_representability_theorem wikiPageWikiLink Grothendieck_duality_theorem.
- Browns_representability_theorem wikiPageWikiLink Homotopy.
- Browns_representability_theorem wikiPageWikiLink Homotopy_category.
- Browns_representability_theorem wikiPageWikiLink Homotopy_theory.
- Browns_representability_theorem wikiPageWikiLink Jacob_Lurie.
- Browns_representability_theorem wikiPageWikiLink Mapping_cylinder.
- Browns_representability_theorem wikiPageWikiLink Mathematics.
- Browns_representability_theorem wikiPageWikiLink Mayer-Vietoris_sequence.
- Browns_representability_theorem wikiPageWikiLink Mayer–Vietoris_sequence.
- Browns_representability_theorem wikiPageWikiLink Natural_transformation.
- Browns_representability_theorem wikiPageWikiLink Necessary_and_sufficient_condition.
- Browns_representability_theorem wikiPageWikiLink Necessity_and_sufficiency.
- Browns_representability_theorem wikiPageWikiLink Pointed_set.
- Browns_representability_theorem wikiPageWikiLink Pullback_(category_theory).
- Browns_representability_theorem wikiPageWikiLink Quasi-category.
- Browns_representability_theorem wikiPageWikiLink Quasicategory.
- Browns_representability_theorem wikiPageWikiLink Representable_functor.
- Browns_representability_theorem wikiPageWikiLink Singular_cohomology.
- Browns_representability_theorem wikiPageWikiLink Singular_homology.
- Browns_representability_theorem wikiPageWikiLink Spectrum_(homotopy_theory).
- Browns_representability_theorem wikiPageWikiLink Spectrum_(topology).
- Browns_representability_theorem wikiPageWikiLink Triangulated_category.
- Browns_representability_theorem wikiPageWikiLink Weak_equivalence_(homotopy_theory).
- Browns_representability_theorem wikiPageWikiLink Weak_homotopy_equivalence.
- Browns_representability_theorem wikiPageWikiLink Wedge_sum.
- Browns_representability_theorem wikiPageWikiLink Yoneda_lemma.
- Browns_representability_theorem wikiPageWikiLink Yonedas_lemma.
- Browns_representability_theorem wikiPageWikiLinkText "Brown's representability theorem".
- Browns_representability_theorem hasPhotoCollection Browns_representability_theorem.
- Browns_representability_theorem wikiPageUsesTemplate Template:Reflist.
- Browns_representability_theorem subject Category:Category_theory.
- Browns_representability_theorem subject Category:Homotopy_theory.
- Browns_representability_theorem subject Category:Representable_functors.
- Browns_representability_theorem subject Category:Theorems_in_algebraic_topology.
- Browns_representability_theorem comment "In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable functor.More specifically, we are givenF: Hotcop → Set,and there are certain obviously necessary conditions for F to be of type Hom(—, C), with C a pointed connected CW-complex that can be deduced from category theory alone.".
- Browns_representability_theorem label "Brown's representability theorem".
- Browns_representability_theorem sameAs m.043mz_.
- Browns_representability_theorem sameAs Q4975963.
- Browns_representability_theorem sameAs Q4975963.
- Browns_representability_theorem wasDerivedFrom Browns_representability_theoremoldid=645943484.
- Browns_representability_theorem isPrimaryTopicOf Browns_representability_theorem.