The additivity theorem in \(K\)-theory
type: Item
instance of: scholarly article
title: The additivity theorem in \(K\)-theory
zbMATH Open document ID: 1077.19001
author: Kevin Charles Jones
author: Andrea H. Mhoon
author: Rekha Santhanam
author: Barry J. Walker
author: Daniel R. Grayson
author: Young-Soo Kim
published in: \(K\)-Theory
publication date: 2005-04-07T00:00:00Z
review text: The authors give new versions, in the style of Quillen's Theorem A, of \textit{F. Waldhausen's} proof [Lect. Notes Math. 1126, 318--419 (1985; Zbl 0579.18006)] of the additivity theorem for algebraic \(K\)-theory. This is carried out by showing some results that allow to convert a theorem B style proof into a theorem A style proof. The first of these results is Theorem Â showing conditions such that, for any functors of small categories \(f:C\rightarrow D\) and \(g:C\rightarrow E\), the induced functor \((f,g):C\rightarrow D\times E\) is a homotopy equivalence. This theorem is then rewritten for maps of simplicial sets obtaining the simplicial set versions Theorem Â* and Theorem Â\('\).
reviewed by: Antonio R. Garzón
Mathematics Subject Classification ID: 19D06
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 2153881
zbMATH Keywords: additivity theorem
zbMATH Keywords: theorem A style
zbMATH Keywords: theorem B style
zbMATH Keywords: simplicial set
MaRDI profile type: Publication
DOI: 10.1023/B:KTHE.0000037546.39459.CB
description: scientific article; zbMATH DE number 2153881