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arXiv · 2506.18451

Globalization and the biactegory of partial modules

Eliezer Batista·William Hautekiet·Joost Vercruysse
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Abstract

We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the close relation between the dilation of partial modules and Hom-objects arising from this enrichment is investigated. In particular, for finite-dimensional pointed Hopf algebras, the standard dilation of a partial module $M$ is isomorphic to the Hom-object from the monoidal unit to $M$.

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Eliezer Batista, William Hautekiet, Joost Vercruysse. 2025-06-23. Globalization and the biactegory of partial modules. https://arxiv.org/abs/2506.18451

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