PreprintCC BY-NC-SA 4.0arXiv
Homology and higher-order intermediate categories for proper abelian subcategories
Abstract
Without needing a t-structure, we establish natural long exact homology sequences on finite extension windows with ℓ+1 layers of extension-closed proper abelian subcategories, assuming vanishing of negative self-extensions in degrees 1,…,ℓ+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.
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BibTeX
@misc{wu2026homology,
title = {{Homology and higher-order intermediate categories for proper abelian subcategories}},
author = {Zheng-Gang Wu and Xianhui Fu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01155},
eprint = {2610.01155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01155},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Homology and higher-order intermediate categories for proper abelian subcategories
AU - Zheng-Gang Wu
AU - Xianhui Fu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01155
UR - https://arxiv.org/abs/2610.01155
AB - Without needing a t-structure, we establish natural long exact homology sequences on finite extension windows with ℓ+1 layers of extension-closed proper abelian subcategories, assuming vanishing of negative self-extensions in degrees 1,…,ℓ+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.
ER -