作者
Octavio Mendoza Hernández, Edith Corina Sáenz Valadez, Valente Santiago Vargas, María José Souto Salorio
发表日期
2013/4
期刊
Applied Categorical Structures
卷号
21
期号
2
页码范围
119-139
出版商
Springer Netherlands
简介
We introduce and develop an analogous of the Auslander–Buchweitz approximation theory (see Auslander and Buchweitz, Societe Mathematique de France 38:5–37, 1989) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category which are based on the behavior of certain subcategories under finiteness of resolutions and vanishing of Hom-spaces. For example: we establish the existence of preenvelopes (and precovers) in certain triangulated subcategories of The results resemble various constructions and results of Auslander and Buchweitz, and are concentrated in exploring the structure of a triangulated category equipped with a pair where is closed under extensions and ω is a weak-cogenerator in usually under additional conditions. This reduces …
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