Categorical aspects of equivariant homotopy
type: Item
instance of: scholarly article
title: Categorical aspects of equivariant homotopy
zbMATH Open document ID: 0855.18009
DOI: 10.1007/BF00122252
author: J.-M. Cordier
author: Timothy Porter
published in: Applied Categorical Structures
publication date: 1997-02-03T00:00:00Z
review text: Let \({\mathcal A}\) and \({\mathcal C}\) be simplicially enriched categories and \(T:{\mathcal A}^{op} \times{\mathcal A}\to{\mathcal C}\) a simplicially enriched functor. The authors define a homotopy coherent end \(\oint_A T(A,A)\) and dually a homotopy coherent coend \(\oint^A T(A,A)\). In particular, if \({\mathcal A}\) is the orbit category \({\mathcal O} (G)\) of a discrete group \(G\) and \(T\) an \({\mathcal O} (G)\)-diagram of simplicial sets then Elmendorf's coalescence \(c\) [\textit{A. D. Elmendorf}, Trans. Am. Math. Soc. 277, 275-284 (1983; Zbl 0521.57027)] is obtained as the left homotopy Kan extension \[ \oint^{G/H} T(G/H) \overline \otimes G/H. \] At the end, an excellent enriched version of Elmendorf's results is presented.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 934055
zbMATH Keywords: equivariant homotopy
zbMATH Keywords: homotopy coherence
zbMATH Keywords: simplicially enriched categories
zbMATH Keywords: orbit category
MaRDI profile type: Publication
cites work: A general formulation of homotopy limits
cites work: Q3759553
cites work: Vogt's theorem on categories of homotopy coherent diagrams
cites work: Fibrant diagrams, rectifications and a construction of Loday
cites work: Q3491793
cites work: Classifying spaces and fibrations
cites work: Bar and cobar constructions. I
cites work: Algebraic classification of equivariant homotopy 2-types. I
cites work: Some Functorial Constructions on G-Spaces
cites work: Homotopy limits and colimits
description: scientific article; zbMATH DE number 934055