Proper resolutions and Gorensteinness in extriangulated categories

Abstract

Let (\ell ,E,s) be an extriangulated category with a proper class \xi of E-triangles, and W an additive full subcategory of (\ell ,E,s). We provide a method for constructing a proper W\xi-resolution (resp., coproper W\xi- coresolution) of one term in an E-triangle in \xi from that of the other two terms. By using this way, we establish the stability of the Gorenstein category GW\xi in extriangulated categories. These results generalize the work of Z. Y. Huang [J. Algebra, 2013, 393: 142{169] and X. Y. Yang and Z. C. Wang [Rocky Mountain J. Math., 2017, 47: 1013{1053], but the proof is not too far from their case. Finally, we give some applications about our main results.

Keywords

Proper resolution / coproper coresolution / extriangulated categories / Gorenstein categories

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Higher Education Press