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Multiplicative structures on comodules in higher categories

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arxiv 2503.01002 v1 pith:QWAI4GMF submitted 2025-03-02 math.CT math.AT

Takeshi Torii This is my paper · ORCID
classification math.CTmath.AT
keywords inftymathcalcategorycomodulescategoriesmathbfmultiplicativestructures
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abstract

In this paper we study multiplicative structures on comodules over bialgebras in the setting of $\infty$-categories. We show that the $\infty$-category of comodules over an $(\mathcal{O},\mathbf{Ass})$-bialgebra in a mixed $(\mathcal{O},\mathbf{Ass})$-duoidal $\infty$-category has the structure of an $\mathcal{O}$-monoidal $\infty$-category for any $\infty$-operad $\mathcal{O}$.

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Cited by 1 Pith paper

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  1. Fourier--Mukai equivalences for formal groups and elliptic Hochschild homology

    math.AG 2025-04 conditional novelty 8.0 of 10

    A new Fourier-Mukai equivalence identifies the formal-group circle of an elliptic curve with the affinization of the curve, showing that two definitions of elliptic Hochschild homology agree and degenerate to ordinary...

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