Central extensions in semi-abelian categories

DOI10.1016/S0022-4049(02)00127-5zbMath1023.18013MaRDI QIDQ1850093

Dominique Bourn, Marino Gran

Publication date: 2 December 2002

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

zbMATH Keywords

central extensionscrossed modulessemi-abelian categoryabelian objects

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Nonabelian homological algebra (category-theoretic aspects) (18G50) Abelian categories, Grothendieck categories (18E10) Categories of algebras (08C05) Factorization systems, substructures, quotient structures, congruences, amalgams (18A32) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05)

Related Items (24)

An intrinsic approach to the non-abelian tensor product via internal crossed squares ⋮ Torsion theories in homological categories ⋮ Normalities and commutators ⋮ Admissibility of localizations of crossed modules ⋮ Higher central extensions and cohomology ⋮ Relative commutator theory in semi-abelian categories ⋮ A description of the fundamental group in terms of commutators and closure operators ⋮ Protolocalisations of homological categories ⋮ Frattini subobjects and extensions in semi-abelian categories ⋮ On the second cohomology group in semi-abelian categories ⋮ Central reflections and nilpotency in exact Mal'tsev categories ⋮ A semi-abelian extension of a theorem by Takeuchi ⋮ Composites of central extensions form a relative semi-abelian category ⋮ Galois theory and commutators ⋮ Peri-abelian categories and the universal central extension condition ⋮ Precrossed modules and Galois theory ⋮ Universal central extensions in semi-abelian categories ⋮ Baer invariants and cohomology of precrossed modules ⋮ Universal central extensions of internal crossed modules via the non-abelian tensor product ⋮ Crossed squares of cocommutative Hopf algebras ⋮ Action representability of the category of internal groupoids ⋮ Protoadditive functors, derived torsion theories and homology ⋮ Commutators and central extensions in universal algebra ⋮ Semi-localizations of semi-abelian categories

Cites Work

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• Groups with Multiple Operators
• H₂(T, G, ∂) and central extensions for crossed modules
• Baer-Invariants of Algebras
• \(3\times 3\) lemma and protomodularity
• Semi-abelian categories

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