Abstract
Let H be a weak Hopf algebra, let C be a weak right H-module coalgebra, and let \( \bar C = {C \mathord{\left/ {\vphantom {C C}} \right. \kern-\nulldelimiterspace} C} \cdot Ker \sqcap ^L \). We prove a structure theorem for weak module coalgebras, namely, C is isomorphic as a weak right H-module coalgebra to a weak smash coproduct \( \bar C \) × H defined on a k-space
if there exists a weak right H-module coalgebra map ϕ: C → H.
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The text was submitted by the authors in English.
Published in Russian in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 3–17.
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Wang, Y., Zhang, L.Y. The structure theorem for weak module coalgebras. Math Notes 88, 3–15 (2010). https://doi.org/10.1134/S0001434610070011
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DOI: https://doi.org/10.1134/S0001434610070011