A description of the fundamental group in terms of commutators and closure operators

DOI10.1016/j.jpaa.2012.02.022zbMath1257.18012arXiv1410.3218OpenAlexW2031715942MaRDI QIDQ456857

Marino Gran, Mathieu Duckerts, Tomas Everaert

Publication date: 16 October 2012

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

Full work available at URL: https://arxiv.org/abs/1410.3218

zbMATH Keywords

Galois groupfundamental groupclosure operatorcommutatorBirkhoff subcategorycategorical Galois theoryhigher Hopf formulaprotoadditive functortorsion-free subcategory

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

A torsion theory in the category of cocommutative Hopf algebras ⋮ Higher coverings of racks and quandles. II ⋮ Fundamental group functors in descent-exact homological categories ⋮ Dual closure operators and their applications ⋮ Protoadditive functors, derived torsion theories and homology ⋮ Epireflective subcategories and formal closure operators

Cites Work

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• Galois theory and commutators
• 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
• On low-dimensional homology in categories
• Pure Galois theory in categories
• Galois groups, abstract commutators, and Hopf formula
• Sheaves in geometry and logic: a first introduction to topos theory
• Galois theory and a general notion of central extension
• Central extensions and internal groupoids in Maltsev categories
• Central extensions in semi-abelian categories
• Protoadditive functors, derived torsion theories and homology
• Higher Hopf formulae for homology via Galois theory
• On satellites in semi-abelian categories: Homology without projectives
• \(3\times 3\) lemma and protomodularity
• Semi-abelian categories