Derived graded modules

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Ryo Ishizuka, Shou Yoshikawa
DOI: 10.48550/arxiv.2601.19164
Cited by: 0

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 $R$.

Fields of Study & Subjects

Algebraic structures and combinatorial models Homotopy and Cohomology in Algebraic Topology Advanced Topics in Algebra

Publication details

Journal / source
arXiv (Cornell University)
Publication date
27 January 2026
Document type
Preprint