Complexes of categories with Abelian group structure

DOI10.1016/0022-4049(83)90030-0zbMath0513.18012OpenAlexW1964394526MaRDI QIDQ1050448

K.-H. Ulbrich, Mitsuhiro Takeuchi

Publication date: 1983

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(83)90030-0

zbMATH Keywords

coherence theorem for complexes of categories with Abelian group structurecommutative ring extensionexact cohomology sequencesHattori-Villamayor-Zelinsky sequencesmapping cone method

Mathematics Subject Classification ID

(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Chain complexes (category-theoretic aspects), dg categories (18G35)

Related Items

Singular extensions and the second cohomology categorical group ⋮ Cohomology with coefficients in stacks of abelian 2-groups ⋮ On the Teichmüller cocycle map ⋮ Chain complexes of symmetric categorical groups ⋮ Categorical \(G\)-crossed modules and 2-fold extensions ⋮ Group cohomology for Picard groups ⋮ Unnamed Item ⋮ Kohärenz in Kategorien mit Gruppenstruktur. III ⋮ A Picard-Brauer exact sequence of categorical groups ⋮ Brauer groups and Galois cohomology for a Krull scheme ⋮ Cohomology with coefficients in symmetric cat-groups. An extension of Eilenberg–MacLane's classification theorem

Cites Work

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• Some arithmetical applications of groups \(H^ q(\)R,G)
• On Amitsur cohomology of rings of algebraic integers
• Brauer groups and Amitsur cohomology for general commutative ring extensions
• Group Extensions By Primary Abelian Groups
• On Villamayor and Zelinsky’s long exact sequence