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arXiv · 2610.01155

Homology and higher-order intermediate categories for proper abelian subcategories

Zheng-Gang Wu·Xianhui Fu
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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.

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Zheng-Gang Wu, Xianhui Fu. 2026-10-01. Homology and higher-order intermediate categories for proper abelian subcategories. https://arxiv.org/abs/2610.01155

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