A Dold-Kan theorem for crossed complexes

DOI10.1016/0022-4049(89)90143-6zbMath0679.18005OpenAlexW2151970258MaRDI QIDQ1822606

Gary Nan Tie

Publication date: 1989

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(89)90143-6

zbMATH Keywords

crossed complexesDold-Kan functorgeneralized Dold-Kan theoremhomotopy preserving equivalenceMoore complex functorsimplicial groupoidsT-groupoids

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05)

Related Items

Varieties of simplicial groupoids. I: Crossed complexes, Homotopy theory, and change of base for groupoids and multiple groupoids, Group-theoretic algebraic models for homotopy types, Crossed Complexes and Higher Homotopy Groupoids as Noncommutative Tools for Higher Dimensional Local-to-Global Problems, The classifying space of a crossed complex, A Dold-Kan theorem for crossed complexes, Iterated \(\bar W\) and T-groupoids, Computation and homotopical applications of induced crossed modules

Cites Work

• Modules croisés généralisés de longueur 2
• Tensor products and homotopies for \(\omega\)-groupoids and crossed complexes
• On the algebra of cubes
• A Dold-Kan theorem for crossed complexes
• Iterated \(\bar W\) and T-groupoids
• Some relations between homology and homotopy groups
• Simplicial methods and the interpretation of “triple” cohomology
• Groupoids as Coefficients
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