Year: 2026
Type: preprint
Abstract: Without needing a $t$-structure, we establish natural long exact homology sequences on finite extension windows with $\ell+1$ layers of extension-closed proper abelian subcategories, assuming vanishing of negative self-extensions in degrees $1,\ldots,\ell+1$, and prove uniform sharpness of this bound. In the Krull-Schmidt setting, we classify intermediate subcategories stable under taking pure homology layers by compatible sequences.
Source: arXiv (Cornell University)
Authors: Wu, Zheng-Gang, Fu, Xianhui
Institutions: Northeast Normal University, Beijing Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215740074