Categorical and simplicial constructions and dualization in algebraic K-theory
type: Item
instance of: scholarly article
title: Categorical and simplicial constructions and dualization in algebraic K-theory
zbMATH Open document ID: 1001.19002
DOI: 10.1023/A:1014050817962
author: Alexander Nenashev
published in: \(K\)-Theory
publication date: 2002-08-21T00:00:00Z
review text: There are several ways to construct the algebraic \(K\)-theory of an exact category \(\mathcal A\). A construction \(T\) is called self-dual if there are good isomorphisms between \(T(\mathcal A)\) and \(T({\mathcal A}^{\text{op}})\). The author describes the extent to which various already known constructions are self-dual. In particular the Gillet-Grayson \(G\)-construction is not self-dual, but the author obtains a new self-dual construction \(W({\mathcal A})\) by combining \(G({\mathcal A})\) and \(G({\mathcal A}^{\text{op}})\). When \({\mathcal A}\) is an exact category with duality, he uses \(W({\mathcal A})\) to describe the duality automorphism of \(K_1({\mathcal A})\) in terms of double exact sequences.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 19D99
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 19D06
Mathematics Subject Classification ID: 18G10
zbMATH DE Number: 1785681
zbMATH Keywords: exact category
zbMATH Keywords: algebraic K-theory
zbMATH Keywords: self-duality
zbMATH Keywords: double exact sequence
MaRDI profile type: Publication
full work available at URL: a:1014050817962
OpenAlex ID: W2021574993
description: scientific article; zbMATH DE number 1785681