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arXiv · 2601.19164

Derived graded modules

Ryo Ishizuka·Shou Yoshikawa
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Abstract

We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free abelian group $G$, and we study its foundational properties. Moreover, we prove a categorical equivalence between (complete) derived $G$-graded modules over $R$ and derived (formal) comodules over a certain comonad constructed from the group ring $R[G]$ of $G$ over $R$.

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Ryo Ishizuka, Shou Yoshikawa. 2026-01-27. Derived graded modules. https://arxiv.org/abs/2601.19164

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