Hermitian \(\mathcal{U}\)-theory of exact categories with duality functors
type: Item
instance of: scholarly article
title: Hermitian \(\mathcal{U}\)-theory of exact categories with duality functors
zbMATH Open document ID: 0854.19004
DOI: 10.1016/0022-4049(95)00093-3
author: Jack M. Shapiro
author: Dongyuan Yao
published in: Journal of Pure and Applied Algebra
publication date: 1997-01-22T00:00:00Z
review text: Let \({\mathcal M}\) be an exact category with a duality functor \(*: {\mathcal M}^{op} \to {\mathcal M}\). Using an analog of Waldhausen's simplicial set approach to \(K\)-theory [cp. \textit{F. Waldhausen}, ``Algebraic \(K\)-theory of spaces'', Lect. Notes Math. 1126, 318-419 (1985; Zbl 0579.18006)] the authors give a new definition of the \({\mathcal U}\)-theory for the category \({\mathcal M}\), defined previously by \textit{M. Uridiya} via the analog of Quillen's \(Q\)-construction [cp. ``\({\mathcal U}\)-theory of exact categories'', Lect. Notes Math. 1437, 303-313 (1990; Zbl 0726.18006)].
Mathematics Subject Classification ID: 19G38
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 18G30
zbMATH DE Number: 896560
zbMATH Keywords: simplicial sets
zbMATH Keywords: category with duality
zbMATH Keywords: \({\mathcal U}\)-theory
reviewed by: Manfred Kolster
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00093-3
OpenAlex ID: W2081981979
cites work: On a theorem of Giffen
cites work: The loop space of the Q-construction
cites work: Weight filtrations via commuting automorphisms
cites work: Q5182334
cites work: Théorie de Quillen et homologie du groupe orthogonal
cites work: Quadratic and Hermitian forms in additive and Abelian categories
cites work: Q3348173
cites work: Q3701607
description: scientific article; zbMATH DE number 896560