Crossed Complexes and Higher Homotopy Groupoids as Noncommutative Tools for Higher Dimensional Local-to-Global Problems

DOI10.1016/S1570-7954(08)00203-9zbMath1214.18014OpenAlexW2145043434MaRDI QIDQ3053860

Ronald Brown

Publication date: 30 October 2010

Published in: Handbook of Algebra - Volume 6 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1570-7954(08)00203-9

zbMATH Keywords

crossed complexeshigher homotopy groupoids

Mathematics Subject Classification ID

Related Items (2)

Variations on a theme of homotopy ⋮ Homology groups of cubical sets with connections

Uses Software

• GAP
• Gpd

Cites Work

• On relative homotopy groups of the product filtration, the James construction, and a formula of Hopf
• Tensor categories attached to double groupoids.
• Normalisation for the fundamental crossed complex of a simplicial set
• Formal homotopy quantum field theories. I: Formal maps and crossed \(\mathcal{C}\)-algebras.
• Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups
• On the homotopy type and the fundamental crossed complex of the skeletal filtration of a CW-complex
• A colimit of classifying spaces
• Coproducts of crossed P-modules: applications to second homotopy groups and to the homology of groups
• Tensor products and homotopies for \(\omega\)-groupoids and crossed complexes
• Van Kampen theorems for diagrams of spaces
• Homotopy classification the J. H. C. Withehead way
• Automorphisms of group extensions and differentials in the Lyndon-Hochschild-Serre spectral sequence
• Crossed \(n\)-fold extensions of groups and cohomology
• Cohomology of groups relative to a variety
• On the algebra of cubes
• Colimit theorems for relative homotopy groups
• Spaces with finitely many non-trivial homotopy groups
• Group-theoretic algebraic models for homotopy types
• Groupoids and crossed objects in algebraic topology
• Erratum to: ``Varieties of simplicial groupoids. I: Crossed complexes
• Van Kampen theorems for categories of covering morphisms in lextensive categories
• Spaces of maps into classifying spaces for equivariant crossed complexes
• Varieties of simplicial groupoids. I: Crossed complexes
• Topological deformation of higher dimensional automata
• Cubical Abelian groups with connections are equivalent to chain complexes
• Towards a 2-dimensional notion of holonomy.
• van Kampen theorems for toposes
• Galois theory and a new homotopy double groupoid of a map of spaces
• The petit topos of globular sets
• A Dold-Kan theorem for crossed complexes
• Multiple categories: The equivalence of a globular and a cubical approach
• Holonomy and parallel transport for abelian gerbes
• Derived functors and the homology of \(n\)-types
• Computation and homotopical applications of induced crossed modules
• On the Eilenberg-Zilber theorem for crossed complexes
• \(n\)-types of simplicial groups and crossed \(n\)-cubes
• A new higher homotopy groupoid: the fundamental globular \(\omega\)-groupoid of a filtered space
• Algebraic topology and concurrency
• Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
• The derived module of a homomorphism
• Cubical structures, homotopy theory
• Categorical homotopy theory
• On adding relations to homotopy groups
• Über Identitäten von Relationen
• Über Identitäten zwischen Relationen
• On mappings into spaces in which certain homotopy groups vanish
• Crossed complexes and chain complexes with operators
• ABSTRACT HOMOTOPY. II
• The classifying space of a crossed complex
• Resolutions of Spaces by Cubes of Fibrations
• Homotopical Excision, and Hurewicz Theorems, for n -Cubes of Spaces
• From Groups to Groupoids: a Brief Survey
• Algebraic Models of 3‐Types and Automorphism Structures for Crossed Modules
• Quotients of groupoids by an action of a group
• Non-Abelian Homological Algebra I. Derived Functors and Satellites
• On the Second Relative Homotopy Group of an Adjunction Space: An Exposition of a Theorem of J. H. C. Whitehead
• Group extensions, crossed pairs and an eight term exact sequence.
• On the Connection between the Second Relative Homotopy Groups of Some Related Spaces
• Free Crossed Resolutions of Groups and Presentations of Modules of Identities among Relations
• Three-Dimensional Presentations for the Groups of Order at Most 30
• On the twisted cobar construction
• The Group Fixed by a Family of Injective Endomorphisms of a Free Group
• Complicial sets characterising the simplicial nerves of strict 𝜔-categories
• Groupoids and Van Kampen's Theorem
• Sur la Cohomologie Non Abelienne, II
• Algebras with a Scheme of Operators
• On the 3-Type of a Complex
• Combinatorial homotopy. I
• Combinatorial homotopy. II
• Simple Homotopy Types
• ABSTRACT HOMOTOPY
• Spaces of maps into classifying spaces for equivariant crossed complexes. II: The general topological group case
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