On exact categories and applications to triangulated adjoints and model structures
Category Theory
2011-07-28 v2 Algebraic Geometry
Algebraic Topology
Representation Theory
Abstract
We show that Quillen's small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model structures. In particular, the interplay of different exact structures on the category of complexes of quasi-coherent sheaves leads to a streamlined and generalized version of recent results obtained by Estrada, Gillespie, Guil Asensio, Hovey, J{\o}rgensen, Neeman, Murfet, Prest, Trlifaj and possibly others.
Cite
@article{arxiv.1005.3248,
title = {On exact categories and applications to triangulated adjoints and model structures},
author = {Manuel Saorin and Jan Stovicek},
journal= {arXiv preprint arXiv:1005.3248},
year = {2011}
}
Comments
38 pages; version 2: major revision, more explanation added at several places, reference list updated and extended, misprints corrected