Spectra of small categories and infinite loop space machines
type: Item
instance of: scholarly article
title: Spectra of small categories and infinite loop space machines
zbMATH Open document ID: 1121.55008
author: Elias Gabriel Minian
published in: \(K\)-Theory
publication date: 2007-02-13T00:00:00Z
review text: The paper is a continuation of a series publications [J. Pure Appl. Algebra 167, No.~2--3, 301--314 (2002; Zbl 1009.18012), Topology Appl. 119, No.~1, 41--51 (2002; Zbl 0993.55004), Appl. Categ. Struct. 11, No.~2, 207--218 (2003; Zbl 1024.18006), \(K\)-Theory 36, No.~3--4, 209--222 (2005; Zbl 1117.55019)] in which the author developed various aspects of the homotopy theory of small categories. This homotopy theory is built around the strong notion of homotopy of functors, i.e. where functors are homotopic if and only if they are linked by a zig-zag of natural transformations. The present article describes how certain concepts of stable homotopy theory can be translated into this context. The author defines a spectrum of small categories and shows that the machinery of special \(\Gamma\)-spaces of Segal can be applied to construct such spectra.
reviewed by: Bernard Badzioch
Mathematics Subject Classification ID: 55P99
Mathematics Subject Classification ID: 55P47
Mathematics Subject Classification ID: 55P48
Mathematics Subject Classification ID: 18G99
zbMATH DE Number: 5125378
zbMATH Keywords: gamma spaces
zbMATH Keywords: small categories
zbMATH Keywords: infinite loop spaces
MaRDI profile type: Publication
full work available at URL: s10977-006-0017-0
OpenAlex ID: W2025001085
cites work: Homotopietheorie
cites work: Partitions of unity in the theory of fibrations
cites work: Q3995201
cites work: Q4095034
cites work: The uniqueness of infinite loop space machines
cites work: \({\mathcal C}at\) as a \(\Lambda\)-cofibration category
cites work: Complexes in Cat
cites work: Loop and suspension functors for small categories and stable homotopy groups
cites work: Numerably contractible categories
cites work: Higher algebraic K-theory: I
cites work: Classifying spaces and spectral sequences
cites work: Categories and cohomology theories
cites work: Q3927379
DOI: 10.1007/S10977-006-0017-0
description: scientific article; zbMATH DE number 5125378