How to construct a Hovey triple from two cotorsion pairs

James Gillespie. "How to construct a Hovey triple from two cotorsion pairs." Fundamenta Mathematicae 230.3 (2015): 281-289. <http://eudml.org/doc/282989>.

@article{JamesGillespie2015,
abstract = {Let be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs $(,\widetilde\{\})$ and $(\widetilde\{\},)$ in satisfying $\widetilde\{\} ⊆ $ and $ ∩ \widetilde\{\} = \widetilde\{\} ∩ $. We show how to construct a (necessarily unique) abelian model structure on with (resp. $\widetilde\{\}$) as the class of cofibrant (resp. trivially cofibrant) objects, and (resp. $\widetilde\{\}$) as the class of fibrant (resp. trivially fibrant) objects.},
author = {James Gillespie},
journal = {Fundamenta Mathematicae},
keywords = {abelian model category; Hovey triple; cotorsion pair},
language = {eng},
number = {3},
pages = {281-289},
title = {How to construct a Hovey triple from two cotorsion pairs},
url = {http://eudml.org/doc/282989},
volume = {230},
year = {2015},
}

TY - JOUR
AU - James Gillespie
TI - How to construct a Hovey triple from two cotorsion pairs
JO - Fundamenta Mathematicae
PY - 2015
VL - 230
IS - 3
SP - 281
EP - 289
AB - Let be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs $(,\widetilde{})$ and $(\widetilde{},)$ in satisfying $\widetilde{} ⊆ $ and $ ∩ \widetilde{} = \widetilde{} ∩ $. We show how to construct a (necessarily unique) abelian model structure on with (resp. $\widetilde{}$) as the class of cofibrant (resp. trivially cofibrant) objects, and (resp. $\widetilde{}$) as the class of fibrant (resp. trivially fibrant) objects.
LA - eng
KW - abelian model category; Hovey triple; cotorsion pair
UR - http://eudml.org/doc/282989
ER -