# DEPTH FOR TRIANGULATED CATEGORIES

• Liu, Yanping (Department of Mathematics, Northwest Normal University) ;
• Liu, Zhongkui (Department of Mathematics, Northwest Normal University) ;
• Yang, Xiaoyan (Department of Mathematics, Northwest Normal University)
• Published : 2016.03.31
• 75 11

#### Abstract

Recently a construction of local cohomology functors for compactly generated triangulated categories admitting small coproducts is introduced and studied by Benson, Iyengar, Krause, Asadollahi and their coauthors. Following their idea, we introduce the depth of objects in such triangulated categories and get that when (R, m) is a graded-commutative Noetherian local ring, the depth of every cohomologically bounded and cohomologically finite object is not larger than its dimension.

#### Keywords

triangulated category;depth;dimension

#### Acknowledgement

Supported by : National Natural Science Foundation of China

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