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MODEL STRUCTURES ON TRIANGULATED CATEGORIES

Part of: Abelian categories Homological algebra Applied homological algebra and category theory

Published online by Cambridge University Press:  18 December 2014

XIAOYAN YANG
XIAOYAN YANG*
Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China e-mail: yangxy@nwnu.edu.cn
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Abstract

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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.

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Secondary: 55U35: Abstract and axiomatic homotopy theory 18G25: Relative homological algebra, projective classes
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 263 - 284
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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