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arXiv · 2610.26196

Simple-shifted monoidal derived equivalences for tensor categories

Jing Yu
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Abstract

In this paper, we investigate monoidal derived equivalences between tensor categories with infinitely many isomorphism classes of simple objects. We introduce the notion of a simple-shifted monoidal derived equivalence and prove that a simple-shifted monoidal derived equivalence gives rise to a tensor equivalence. In addition, we investigate which tensor categories have the property that every monoidal derived equivalence between them is necessarily simple-shifted, and we establish some sufficient conditions for this property. As a corollary, we show that a monoidal derived equivalence between pointed tensor categories implies a tensor equivalence between them.

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Jing Yu. 2026-10-19. Simple-shifted monoidal derived equivalences for tensor categories. https://arxiv.org/abs/2610.26196

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