On exact categories and applications to triangulated adjoints and model structures

Details On exact categories and applications to triangulated adjoints and model structures On exact categories and applications to triangulated adjoints and model structures

2010-05-18

arxiv.org/abs/1005.3248v2

Adv. Math. 228 (2011) 968-1007

Mathematics

Category Theory

38 pages; version 2: major revision, more explanation added at several places, reference list updated and extended, misprints

Scientific paper

10.1016/j.aim.2011.05.025

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.

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