Special Precovered Categories of Gorenstein Categories
Tiwei Zhao, Zhaoyong Huang

TL;DR
This paper investigates special precovering categories related to Gorenstein categories within an abelian category, establishing their closure properties and resolving structures under certain conditions.
Contribution
It introduces and characterizes special Gorenstein precovering subcategories, showing their closure under extensions and their resolving properties in abelian categories.
Findings
The right 1-orthogonal of Gorenstein subcategories is projectively resolving.
The subcategory of objects with special Gorenstein precovers is extension-closed.
Under certain conditions, this subcategory is minimal and resolving with a proper generator.
Abstract
Let be an abelian category and the subcategory of consisting of projective objects. Let be a full, additive and self-orthogonal subcategory of with a generator, and let be the Gorenstein subcategory of . Then the right 1-orthogonal category of is both projectively resolving and injectively coresolving in . We also get that the subcategory of consisting of objects admitting special -precovers is closed under extensions and -stable direct summands (*). Furthermore, if is a generator for , then we have that…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology
