Globalization for geometric partial comodules

We discuss globalization for geometric partial comodules in a monoidal category with pushouts and we provide a concrete procedure to construct it, whenever it exists. The mild assumptions required by our approach make it possible to apply it in a number of contexts of interests, recovering and exten...

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Bibliographic Details
Published in:Journal of algebra 2022-07, Vol.602, p.37-59
Main Authors: Saracco, Paolo, Vercruysse, Joost
Format: Article
Language:English
Subjects:
Coalgebra
Geometric partial comodule
Globalization
Monoidal category
Partial action
Partial comodule algebra
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Summary:We discuss globalization for geometric partial comodules in a monoidal category with pushouts and we provide a concrete procedure to construct it, whenever it exists. The mild assumptions required by our approach make it possible to apply it in a number of contexts of interests, recovering and extending numerous ad hoc globalization constructions from the literature in some cases and providing obstruction for globalization in some other cases.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.03.013