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arXiv · 2606.19485

Hopfological algebra, revisited

Juan Omar Gómez·Gustavo Jasso·Marius Nielsen
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Abstract

We propose an $\infty$-categorical approach to Khovanov--Qi's Hopfological algebra that, in particular, refines several foundational aspects of the theory by recasting the previous constructions in terms of $\infty$-categories of modules in monoidal $\infty$-categories. This perspective leads to a more general variant of Hopfological algebra that takes place over an arbitrary rigidly-compactly generated symmetric monoidal stable $\infty$-category, which we also outline in the article. In the appendix, we compare the construction of Hopfological derived categories to that of Holm--J{\o}rgensen's $Q$-shaped derived categories.

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Juan Omar Gómez, Gustavo Jasso, Marius Nielsen. 2026-06-17. Hopfological algebra, revisited. https://arxiv.org/abs/2606.19485

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