Approximations and adjoints in homotopy categories
Category Theory
2010-06-24 v2 Algebraic Topology
Representation Theory
Abstract
We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy categories. Applications include the study of (pure) derived categories. For instance, it is shown that the pure derived category of any module category is compactly generated.
Cite
@article{arxiv.1005.0209,
title = {Approximations and adjoints in homotopy categories},
author = {Henning Krause},
journal= {arXiv preprint arXiv:1005.0209},
year = {2010}
}
Comments
15 pages, added some remarks, another description of the pure derived category of a module category, and an example