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arXiv · 2602.07368

Silting and tilting objects in cleft extensions of abelian categories

Guoqiang Zhao·Juxiang Sun
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Abstract

We establish connections between silting and tilting objects in an abelian category $\mathcal{B}$ and those in a cleft extension $\mathcal{A}$ of $\mathcal{B}$, which provides a method for constructing more silting and tilting objects. Then we apply our results to the cleft extensions of module categories, and characterize silting and tilting modules over $\theta$-extension of rings. Some known results over trivial extension of rings are extended and strengthened.

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Guoqiang Zhao, Juxiang Sun. 2026-02-07. Silting and tilting objects in cleft extensions of abelian categories. https://arxiv.org/abs/2602.07368

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