Geometric partial comodules over flat coalgebras in Abelian categories are globalizable |
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| Affiliation: | 1. Université de Reims, Laboratoire de Mathématiques (UMR 9008 - CNRS), Moulin de la Housse, B.P. 1039, 51687 Reims cedex 2, France;2. Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France;1. College of Science, Jinling Institute of Technology, Nanjing 211169, China;2. Department of Mathematics, Wenzhou University, Wenzhou 325035, China;3. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;4. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China;1. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, RO-010014 Bucharest 1, Romania;2. Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania;1. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Via Trieste 63, 35121 Padova, Italy;2. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic |
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| Abstract: | 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. |
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| Keywords: | Globalization Partial (co)action and (co)representation Geometric partial comodule Abelian category Hopf algebra Non-coassociative comodule |
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