Derived functors and the homology of \(n\)-types

DOI10.1016/S0021-8693(02)00048-0zbMath1010.18009OpenAlexW2091395363MaRDI QIDQ1858237

Manuel Ladra Gonzalez, Graham J. Ellis, José Manuel Casas Mirás, Teimouraz Pirashvili

Publication date: 12 February 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(02)00048-0

zbMATH Keywords

abelianisationcrossed n-cube\(\text{cat}^n\)-grouphomotopy n-type

Mathematics Subject Classification ID

Classification of homotopy type (55P15) Homological methods in group theory (20J05)

Related Items

Some aspects of homotopic algebra and non-abelian (co)homology theories ⋮ Weakly globular \(\text{cat}^n\)-groups and Tamsamani's model ⋮ Computing group resolutions. ⋮ Homotopical and combinatorial aspects of the theory of normal series in groups. ⋮ Homology of \((n+1)\)-types and Hopf type formulas ⋮ COTRIPLE HOMOLOGY OF CROSSED 2-CUBES OF LIE ALGEBRAS ⋮ Homological aspects of Lie algebra crossed modules ⋮ Crossed Complexes and Higher Homotopy Groupoids as Noncommutative Tools for Higher Dimensional Local-to-Global Problems

Cites Work

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• Higher-dimensional crossed modules and the homotopy groups of \((n+1)\)- ads
• Spaces with finitely many non-trivial homotopy groups
• (Co)homology of crossed modules with coefficients in a \(\pi_1\)-module
• CCG-homology of crossed modules via classifying spaces
• \(n\)-types of simplicial groups and crossed \(n\)-cubes
• Spectral sequences of a double semi-simplicial group
• Homotopical algebra
• Homology of 2-Types
• Hopf Formulae for the Higher Homology of a Group
• On (co)homology of 2-types and crossed modules
• (Co)Homology of crossed modules

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