Gorenstein syzygy objects in extriangulated categories
Peiyu Zhang, Ming Chen, Dajun Liu, Jiaqun Wei
TL;DR
This paper introduces Gorenstein syzygy objects within extriangulated categories, providing a new characterization and exploring their behavior under recollements, thus extending the understanding of Gorenstein homological algebra in this context.
Contribution
It defines Gorenstein syzygy objects in extriangulated categories and demonstrates their properties and behavior under recollements, offering new insights into Gorenstein homological structures.
Findings
Gorenstein syzygy objects are characterized in extriangulated categories.
Under certain conditions, Gorenstein syzygy objects induce new such objects in recollements.
The paper establishes the behavior of Gorenstein syzygy objects in complex categorical structures.
Abstract
We give the definition of Gorenstein syzygy objects in extriangulated categories and obtain a characterization. For a recollement of extriangulated categories, we mainly show that Gorenstein syzygy objects induce a new Gorenstein syzygy objects under certain conditions, and prove that Gorenstein syzygy objects induce a new Gorenstein syzygy objects under certain conditions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Commutative Algebra and Its Applications