Abstract
Let (\(\mathscr{C},\mathbb{E},\frak{s}\)) be an extriangulated category with a proper class ξ of \(\mathbb{E}\)-triangles, and \(\mathscr{W}\) an additive full subcategory of (\(\mathscr{C},\mathbb{E},\frak{s}\)). We provide a method for constructing a proper \(\mathscr{W}\)(ξ)-resolution (resp., coproper \(\mathscr{W}\)(ξ)-coresolution) of one term in an \(\mathbb{E}\)-triangle in ξ from that of the other two terms. By using this way, we establish the stability of the Gorenstein category \(\mathscr{G}\mathscr{W}\)(ξ) 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
