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2017 Proper resolutions and Gorensteinness in triangulated categories
Xiaoyan Yang, Zhicheng Wang
Rocky Mountain J. Math. 47(3): 1013-1053 (2017). DOI: 10.1216/RMJ-2017-47-3-1013

Abstract

Let $\mathcal {T}$ be a triangulated category with triangulation $\Delta $, $\xi \subseteq \Delta $ a proper class of triangles and $\mathcal {C}$ an additive full subcategory of $\mathcal {T}$. We provide a method for constructing a proper $\mathcal {C}(\xi )$-resolution (respectively, coproper $\mathcal {C}(\xi )$-coresolution) of one term in a triangle in $\xi $ from those of the other two terms. By using this construction, we show the stability of the Gorenstein category $\mathcal {GC}(\xi )$ in triangulated categories. Some applications are given.

Citation

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Xiaoyan Yang. Zhicheng Wang. "Proper resolutions and Gorensteinness in triangulated categories." Rocky Mountain J. Math. 47 (3) 1013 - 1053, 2017. https://doi.org/10.1216/RMJ-2017-47-3-1013

Information

Published: 2017
First available in Project Euclid: 24 June 2017

zbMATH: 06741631
MathSciNet: MR3682160
Digital Object Identifier: 10.1216/RMJ-2017-47-3-1013

Subjects:
Primary: 18E30, 18G10, 18G25

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 3 • 2017
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