On the Karoubi filtration of a category
type: Item
instance of: scholarly article
title: On the Karoubi filtration of a category
zbMATH Open document ID: 0903.18005
DOI: 10.1023/A:1007726201728
published in: \(K\)-Theory
publication date: 1998-12-09T00:00:00Z
review text: There is a notion, due to Karoubi, of an additive category \({\mathcal U}\) being filtered by a full subcategory \({\mathcal A}\); it is the categorical analogue of an ideal \({\mathcal A}\) in a ring \({\mathcal U}\). When \({\mathcal U}\) and \({\mathcal A}\) are such categories, there are fibrations of spectra giving \(K\)-theory exact sequences associated to the sequence \({\mathcal A}\to{\mathcal U}\to{\mathcal U}/{\mathcal A}\); these fibrations have been used to prove excision results. In this paper the authors give new proofs for the fibrations based on Waldhausen's \(S\)-construction and generic fibration lemma.
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 19D10
zbMATH DE Number: 1062414
zbMATH Keywords: \(K\)-theory spectra
zbMATH Keywords: Karoubi filtration
zbMATH Keywords: excision
zbMATH Keywords: fibrations
author: Manuel Cárdenas
author: Erik K. Pedersen
reviewed by: Richard John Steiner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1062414