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- Mapping_cone_(homological_algebra) abstract "In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain complexes take their terms in an abelian category, so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi-isomorphism; if we pass to the derived category of complexes, this means that f is an isomorphism there, which recalls the familiar property of maps of groups, modules over a ring, or elements of an arbitrary abelian category that if the kernel and cokernel both vanish, then the map is an isomorphism. If we are working in a t-category, then in fact the cone furnishes both the kernel and cokernel of maps between objects of its core.".
- Mapping_cone_(homological_algebra) wikiPageID "10125391".
- Mapping_cone_(homological_algebra) wikiPageLength "6125".
- Mapping_cone_(homological_algebra) wikiPageOutDegree "35".
- Mapping_cone_(homological_algebra) wikiPageRevisionID "681178364".
- Mapping_cone_(homological_algebra) wikiPageWikiLink Abelian_category.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Acyclic_complex.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Additive_category.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Category:Homological_algebra.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Chain_complex.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Chain_complexes.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Cochain_complexes.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Cohomology.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Cohomology_group.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Cokernel.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Column_vector.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Continuous_function.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Continuous_map.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Derived_category.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Direct_sum.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Exact_sequence.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Group_(mathematics).
- Mapping_cone_(homological_algebra) wikiPageWikiLink Homological_algebra.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Homotopy_category_of_chain_complexes.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Kernel_(category_theory).
- Mapping_cone_(homological_algebra) wikiPageWikiLink Long_exact_sequence.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Mapping_cone_(topology).
- Mapping_cone_(homological_algebra) wikiPageWikiLink Mapping_cylinder.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Module_(mathematics).
- Mapping_cone_(homological_algebra) wikiPageWikiLink Quasi-isomorphism.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Row_and_column_vectors.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Singular_homology.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Springer-Verlag.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Springer_Science+Business_Media.
- Mapping_cone_(homological_algebra) wikiPageWikiLink T-category.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Topological_space.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Triangulated_categories.
- Mapping_cone_(homological_algebra) wikiPageWikiLink Triangulated_category.
- Mapping_cone_(homological_algebra) wikiPageWikiLinkText "Mapping cone (homological algebra)".
- Mapping_cone_(homological_algebra) wikiPageWikiLinkText "cone".
- Mapping_cone_(homological_algebra) wikiPageWikiLinkText "mapping cone (homological algebra)".
- Mapping_cone_(homological_algebra) wikiPageWikiLinkText "mapping cone".
- Mapping_cone_(homological_algebra) hasPhotoCollection Mapping_cone_(homological_algebra).
- Mapping_cone_(homological_algebra) wikiPageUsesTemplate Template:Citation.
- Mapping_cone_(homological_algebra) wikiPageUsesTemplate Template:Weibel_IHA.
- Mapping_cone_(homological_algebra) subject Category:Homological_algebra.
- Mapping_cone_(homological_algebra) hypernym Construction.
- Mapping_cone_(homological_algebra) type Company.
- Mapping_cone_(homological_algebra) comment "In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology.".
- Mapping_cone_(homological_algebra) label "Mapping cone (homological algebra)".
- Mapping_cone_(homological_algebra) sameAs m.02q2m34.
- Mapping_cone_(homological_algebra) sameAs Q6754178.
- Mapping_cone_(homological_algebra) sameAs Q6754178.
- Mapping_cone_(homological_algebra) wasDerivedFrom Mapping_cone_(homological_algebra)?oldid=681178364.
- Mapping_cone_(homological_algebra) isPrimaryTopicOf Mapping_cone_(homological_algebra).