Non-compactly generated categories
type: Item
instance of: scholarly article
title: Non-compactly generated categories
zbMATH Open document ID: 0939.18009
DOI: 10.1016/S0040-9383(97)00069-4
author: Amnon Neeman
published in: Topology
publication date: 2000-07-12T00:00:00Z
review text: The paper answers the following question raised by \textit{J. H. Palmieri} in affirmative: Is there a triangulated category which is not compactly generated? The topological terms ``triangulated'' and ``compactly generated'' are used here in categorical terms, e.g., an object \(c\) of a category \({\mathcal T}\) is called compact if any map from it to any coproduct of objects in \({\mathcal T}\) factors through a finite coproduct. The counterexample produced by the author has many interesting features. He uses in his construction the nice category of \(H\)-local objects where \(H\) is a homology theory. The category of \(H\)-local objects has tensor products which have an adjoint. The counterexample is obtained from the derived category of a commutative local Noetherian integral domain \(R\) of dimension greater than one by localizing \(D(R)\) with respect to the homology theory given by smashing with \(k\oplus K\) where \(k\) is the residue field and \(K\) is the quotient field.
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 13D99
Mathematics Subject Classification ID: 18E35
Mathematics Subject Classification ID: 55N99
Mathematics Subject Classification ID: 54D99
zbMATH DE Number: 1307789
zbMATH Keywords: localizing with respect to homology
zbMATH Keywords: triangulated category
zbMATH Keywords: compactly generated
zbMATH Keywords: homology smashing
zbMATH Keywords: derived category
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1307789