Triple brackets and lax morphism categories
type: Item
instance of: scholarly article
title: Triple brackets and lax morphism categories
zbMATH Open document ID: 1042.18005
DOI: 10.1023/B:APCS.0000013803.33614.67
published in: Applied Categorical Structures
publication date: 2004-05-27T00:00:00Z
review text: The theory of secondary operations in homotopy groups has been extended to the context of a \(2\)-category \({\mathcal C}\) with zeros. In this paper the authors study the lax morphism category \(m{\mathcal C}\), thereby generalising operations in relative homotopy groups. In particular they study Toda brackets in \(m{\mathcal C}\). They consider the behaviour of these brackets when \({\mathcal C}\) has a suspension functor, and they apply their results to homotopy groups of spheres. They also describe two-sided matrix Toda brackets, which are applied to homotopy groups of spheres and to quaternary Toda brackets.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 55Q35
Mathematics Subject Classification ID: 55P40
zbMATH DE Number: 2069037
zbMATH Keywords: Toda bracket
zbMATH Keywords: 2-category
zbMATH Keywords: lax morphism category
zbMATH Keywords: homotopy groups of spheres
author: K. A. Hardie
author: Klaus Heiner Kamps
author: Howard J. Marcum
author: Nobuyuki Oda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2069037