Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

Compactly generated homotopy categories

Pages: 257 – 274

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a11


Henrik Holm (Department of Mathematical Sciences, University of Aarhus, Denmark)

Peter Jørgensen (School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, United Kingdom)


Over an associative ring we consider a class $\mathbb{X}$ of left modules which is closed under set-indexed coproducts and direct summands. We investigate when the triangulated homotopy category $K(\mathbb{X})$ is compactly generated, and give a number of examples.


compactly generated category, compact object, homotopy category, pure exact sequence, triangulated category

2010 Mathematics Subject Classification

16D20, 16D40, 16D50, 16D90, 16E05

Published 1 January 2007