| dbo:abstract |
In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and cokernels, which is necessary for the usual definition of such a sequence. (en) Une catégorie exacte, parfois dite exacte « au sens de Quillen » pour distinguer des (en) (exactes « au sens de (en) ») et des catégories abéliennes (exactes « au sens de Buchsbaum »), est une catégorie englobant et généralisant la notion de suite exacte et de foncteur exact. Les catégories exactes ont été introduites par Daniel Quillen dans le cadre de la K-théorie algébrique. (fr) 호몰로지 대수학에서 퀼런 완전 범주(Quillen完全範疇, 영어: Quillen-exact category)는 짧은 완전열의 개념이 부여된 가법 범주이며, 아벨 범주의 개념의 일반화이다. 아벨 범주의 짧은 완전열들이 만족시키는 성질들을 공리화하여 추상화한 개념이지만, 아벨 범주의 개념과 달리 사상들이 핵 및 여핵을 가질 필요가 없다. 퀼런 완전 범주 위에는 대수적 K이론을 취할 수 있다. (ko) |
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dbr:Pullback_(category_theory) dbr:De_Rham_cohomology dbr:Mathematics dbr:Class_(set_theory) dbr:Short_exact_sequence dbr:Closed_and_exact_differential_forms dbr:Additive_category dbr:Dual_(category_theory) dbr:Additive_functor dbr:Daniel_Quillen dbc:Homological_algebra dbr:Abelian_category dbr:Abelian_group dbc:Additive_categories dbr:Kernel_(category_theory) dbr:Torsion-free_abelian_group dbr:Circle_group dbr:Category_theory dbr:Exact_functor dbr:Pushout_(category_theory) dbr:Yoneda_lemma dbr:Extension_(algebra) dbr:Strictly_full_subcategory dbr:Manuscripta_Mathematica |
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Bernhard (en) |
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Keller (en) Quillen (en) |
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dbc:Homological_algebra dbc:Additive_categories |
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dbr:Concept |
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| rdfs:comment |
In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and cokernels, which is necessary for the usual definition of such a sequence. (en) Une catégorie exacte, parfois dite exacte « au sens de Quillen » pour distinguer des (en) (exactes « au sens de (en) ») et des catégories abéliennes (exactes « au sens de Buchsbaum »), est une catégorie englobant et généralisant la notion de suite exacte et de foncteur exact. Les catégories exactes ont été introduites par Daniel Quillen dans le cadre de la K-théorie algébrique. (fr) 호몰로지 대수학에서 퀼런 완전 범주(Quillen完全範疇, 영어: Quillen-exact category)는 짧은 완전열의 개념이 부여된 가법 범주이며, 아벨 범주의 개념의 일반화이다. 아벨 범주의 짧은 완전열들이 만족시키는 성질들을 공리화하여 추상화한 개념이지만, 아벨 범주의 개념과 달리 사상들이 핵 및 여핵을 가질 필요가 없다. 퀼런 완전 범주 위에는 대수적 K이론을 취할 수 있다. (ko) |
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Exact category (en) Catégorie exacte (fr) 퀼런 완전 범주 (ko) |
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