On the algebraic \(K\)-theory of infinite product categories
type: Item
instance of: scholarly article
title: On the algebraic \(K\)-theory of infinite product categories
zbMATH Open document ID: 0829.18005
DOI: 10.1007/BF00961467
published in: \(K\)-Theory
publication date: 1996-01-17T00:00:00Z
review text: It is shown that the \(K\)-theory functor in the category of symmetric monoidal categories preserves arbitrary products. For finite products, this is an easy observation, but for infinite products one has to work. The work takes place in a simplicial setting and uses Waldhausen's definition of \(K\)-theory in terms of categories with cofibrations, weak equivalences and cylinder functors. It is shown that \(K\)-theory spectra obtained this way are close enough to being Kan for the desired conclusion (which would be easy if all complexes were Kan) to be available.
reviewed by: Hans Jørgen Munkholm
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 19D23
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 18G30
zbMATH DE Number: 800394
zbMATH Keywords: algebraic \(K\)-theory
zbMATH Keywords: Kan complexes
zbMATH Keywords: Waldhausen categories
zbMATH Keywords: \(K\)-theory spectra
zbMATH Keywords: symmetric monoidal categories
zbMATH Keywords: products
zbMATH Keywords: cylinder functors
author: Gunnar Carlsson
MaRDI profile type: Publication
cites work: Homotopy limits, completions and localizations
cites work: On c.s.s. Complexes
description: scientific article; zbMATH DE number 800394