Geometric partial comodules over flat coalgebras in Abelian categories are globalizable

The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial representations of groups and Hopf algebras, our globalization c...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2024-03, Vol.228 (3), p.107502, Article 107502
Main Authors: Saracco, Paolo, Vercruysse, Joost
Format: Article
Language:English
Subjects:
Abelian category
Geometric partial comodule
Globalization
Hopf algebra
Non-coassociative comodule
Partial (co)action and (co)representation
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Summary:The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial representations of groups and Hopf algebras, our globalization coincides with those described earlier in literature. Finally, we introduce Hopf partial comodules over a bialgebra as geometric partial comodules in the monoidal category of (global) modules. By applying our globalization theorem we obtain an analogue of the fundamental theorem for Hopf modules in this partial setting.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2023.107502