Spaces of maps into classifying spaces for equivariant crossed complexes
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In this article, an equivariant version of the homotopy theory of crossed complexes is presented, and the applications generalize work on Equivariant Eilenberg-Mac Lane spaces, including the non abelian case of dimension 1 and on local systems.About:
This article is published in Indagationes Mathematicae.The article was published on 1997-06-23 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Equivariant map & Equivariant cohomology.read more
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Journal ArticleDOI
Groupoids and crossed objects in algebraic topology
TL;DR: In this paper, an introductory survey of the passage from groups to groupoids and their higher dimensional versions is presented, with most emphasis on calculations with crossed modules and the construction and use of homotopy double groupoids.
Journal ArticleDOI
The 1-type of a Waldhausen K-theory spectrum
Fernando Muro,Andrew Tonks +1 more
TL;DR: In this article, a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category is presented.
Book ChapterDOI
Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems ⁄
TL;DR: A survey of results of crossed complexes obtained by R. Brown and P.J. Higgins and others over the years 1974-2008 and its applications and related areas can be found in this paper.
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Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems
TL;DR: In this paper, the main features of crossed complexes and cubical groupoids with connections are defined and applied to algebraic topology and the cohomology of groups with the ability to obtain some non commutative results and compute some homotopy types.
Journal ArticleDOI
Group cohomology with coefficients in a crossed module
TL;DR: In this article, the authors compare three different ways of defining group cohomology with coefficients in a crossed module: (1) explicit approach via cocycles; (2) geometric approach via gerbes; (3) group theoretic approach via butterflies.
References
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Book
Homotopy Limits, Completions and Localizations
A. K. Bousfield,Daniel M. Kan +1 more
TL;DR: The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X, which coincides up to homotopy with the p-profinite completion of Quillen and Sullivan as mentioned in this paper.
Journal ArticleDOI
A Certain Exact Sequence
TL;DR: The sequence 2(X) is followed by the main theorem, which states that the sequence r(A) is equivalent to 2(C, A), and the sequence K is a combination of 2 (C and A) and 2 (A), which are equivalent to 1 (A and C).