Relative Tilting Classes in Extriangulated Categories

In this paper, we study the relative tilting theory in extriangulated categories. We introduce the notion of relative tilting classes in an extriangulated category and then give some equivalent characterizations. On the above basis, we discuss the relations between relative homological dimensions an...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2024-03, Vol.47 (2), Article 50
Main Authors: Wang, Dingguo, Yu, Yuanhui, Zhao, Tiwei
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:In this paper, we study the relative tilting theory in extriangulated categories. We introduce the notion of relative tilting classes in an extriangulated category and then give some equivalent characterizations. On the above basis, we discuss the relations between relative homological dimensions and relative (co)resolution dimensions in the context of relative tilting classes. We also introduce the notion of relative tilting triples, and then discuss the relations between them.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01645-5