Gorenstein projective objects in homotopy categories
Lu Bo, Liu Zhongkui
TL;DR
This paper characterizes Gorenstein projective objects within homotopy categories, demonstrating their structure as a compactly generated triangulated category and establishing an equivalence of such categories over certain rings.
Contribution
It provides a new characterization of Gorenstein projective objects in the category of complexes and proves their category is compactly generated, with an equivalence result over specific rings.
Findings
Gorenstein projective objects form a compactly generated triangulated category.
An equivalence of triangulated categories is established over some rings.
The paper offers a characterization of Gorenstein projective objects in homotopy categories.
Abstract
In this paper, we are concerned with Gorenstein projective objects in homotopy categories. Specifically, we present a characterization on Gorenstein projective objects in the category of complexes. Using this result, it is proved that the category of Gorenstein projective objects is a compactly generated triangulated category and an equivalence of triangulated categories is also given over some reasonably nice rings.
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 · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra