Central support for triangulated categories
Henning Krause
TL;DR
This paper introduces a new notion of central support for triangulated categories, generalizing existing support theories and establishing foundational structures like Mayer-Vietoris sequences for subcategories.
Contribution
It defines the centre of the lattice of thick subcategories, creating a universal framework for cohomological support in triangulated categories.
Findings
Introduces the centre as a spatial frame for triangulated categories.
Recovers support theory for tensor triangulated categories.
Establishes Mayer-Vietoris sequences for commuting subcategories.
Abstract
For any essentially small triangulated category the centre of its lattice of thick subcategories is introduced; it is a spatial frame and yields a notion of central support. A relative version of this centre recovers the support theory for tensor triangulated categories and provides a universal notion of cohomological support. Along the way we establish Mayer-Vietoris sequences for pairs of commuting subcategories.
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 · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology