Protoadditive functors, derived torsion theories and homology

DOI10.1016/j.jpaa.2014.12.015zbMath1341.18005arXiv1111.5448OpenAlexW2145457812MaRDI QIDQ2341557

Marino Gran, Tomas Everaert

Publication date: 24 April 2015

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

Full work available at URL: https://arxiv.org/abs/1111.5448

zbMATH Keywords

semi-abelian categorycategorical Galois theory

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Torsion theories, radicals (18E40) Homological methods in group theory (20J05) Nonabelian homological algebra (category-theoretic aspects) (18G50)

Related Items (20)

A torsion theory in the category of cocommutative Hopf algebras ⋮ Torsion theories and coverings of \(V\)-groups ⋮ Monotone-light factorisation systems and torsion theories ⋮ The Yoneda isomorphism commutes with homology ⋮ Higher central extensions and cohomology ⋮ Universal central extensions of Lie crossed modules over a fixed Lie algebra ⋮ Pretorsion theories in general categories ⋮ CONDITIONAL FLATNESS, FIBERWISE LOCALIZATIONS, AND ADMISSIBLE REFLECTIONS ⋮ Resolutions, higher extensions and the relative Mal'tsev axiom ⋮ Relative commutator theory in semi-abelian categories ⋮ A description of the fundamental group in terms of commutators and closure operators ⋮ Some remarks on protolocalizations and protoadditive reflections ⋮ Fundamental group functors in descent-exact homological categories ⋮ Torsion theories and coverings of preordered groups ⋮ A comonadic interpretation of Baues-Ellis homology of crossed modules ⋮ Universal central extensions of internal crossed modules via the non-abelian tensor product ⋮ Higher commutator conditions for extensions in Mal'tsev categories ⋮ Conditionally flat functors on spaces and groups ⋮ Action representability of the category of internal groupoids ⋮ Semi-localizations of semi-abelian categories

Cites Work

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• Monotone-light factorisation systems and torsion theories
• A description of the fundamental group in terms of commutators and closure operators
• Higher central extensions and Hopf formulae
• Topological semi-abelian algebras
• Torsion theories in homological categories
• Torsion theories and radicals in normal categories
• Torsion theories and Galois coverings of topological groups
• Pure Galois theory in categories
• Protolocalisations of homological categories
• Locally semisimple coverings
• On subtractive varieties. I
• Some remarks on Maltsev and Goursat categories
• Galois theory and a general notion of central extension
• On localization and stabilization for factorization systems
• Affine categories and naturally Mal'cev categories
• Central extensions and internal groupoids in Maltsev categories
• Central extensions in semi-abelian categories
• The denormalized \(3{\times}3\) lemma
• Arithmetical categories and commutator theory
• Mal'cev categories and fibration of pointed objects
• Higher Hopf formulae for homology via Galois theory
• Topological protomodular algebras
• Hopf Formulae for the Higher Homology of a Group
• THE FUNDAMENTAL THEOREM OF GALOIS THEORY
• A Torsion Theory for Abelian Categories
• COMMUTATOR, NILPOTENCY, AND SOLVABILITY IN CATEGORIES
• Homological and homotopical aspects of torsion theories
• Open mappings on locally compact spaces
• Duality for groups
• Exact Categories and Duality
• \(3\times 3\) lemma and protomodularity
• Semi-abelian categories

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