Geodesic
MODEL STRUCTURES ON TRIANGULATED CATEGORIES
Glasgow mathematical journal, Tome 57 (2015) no. 2, pp. 263-284

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DOI

We define model structures on a triangulated category with respect to some proper classes of triangles and give a general study of triangulated model structures. We look at the relationship between these model structures and cotorsion pairs with respect to a proper class of triangles on the triangulated category. In particular, we get Hovey's one-to-one correspondence between triangulated model structures and complete cotorsion pairs with respect to a proper class of triangles. Some applications are given. 
YANG, XIAOYAN. MODEL STRUCTURES ON TRIANGULATED CATEGORIES. Glasgow mathematical journal, Tome 57 (2015) no. 2, pp. 263-284. doi: 10.1017/S0017089514000299
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     author = {YANG, XIAOYAN},
     title = {MODEL {STRUCTURES} {ON} {TRIANGULATED} {CATEGORIES}},
     journal = {Glasgow mathematical journal},
     pages = {263--284},
     year = {2015},
     volume = {57},
     number = {2},
     doi = {10.1017/S0017089514000299},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000299/}
}
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