Universal spaces for homotopy limits of modules over coaugmented functors. I
type: Item
instance of: scholarly article
title: Universal spaces for homotopy limits of modules over coaugmented functors. I
zbMATH Open document ID: 1025.55007
DOI: 10.1016/S0040-9383(02)00019-8
author: Assaf Libman
published in: Topology
publication date: 2003-06-17T00:00:00Z
review text: After the introduction, the author gives the definitions and some facts about cofacial resolutions in section 2. Coaugmented functors are the standard source of cofacial resolutions. The concept of \(J\)-module is defined and is shown to be a source of trivial cofacial resolutions (the ones with left contractions). In section 3 simplicial coaugmented functors are defined, giving several examples and results. The main result of the paper is proved in section 4: homotopy limits of \(J\)-modules are themselves \(J_n\)-modules for suitable functors \(J_n\). Section 5 is dedicated to the definition of generalized Eilenberg MacLane spaces (GEMs) and thin-polyGEMs, and to the investigation of some consequences of the main theorem regarding the unstable Adams spectral sequence of these spaces. The paper concludes with an appendix, where a proof for a special case of theorem \(3.2\) in part II of the present paper [Topology 42, 569-602 (2003; Zbl 1025.55008)] is sketched.
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18A25
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55T15
zbMATH DE Number: 1929316
zbMATH Keywords: homotopy limits
zbMATH Keywords: coaugmented functors
zbMATH Keywords: Bousfield-Kan spectral sequence
reviewed by: J. Remedios
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1929316