Abstract
In this paper we define conditions under which a tensor product $A \otimes H$, in a braided monoidal category, together with a crossed product structure $A \mathbin{\sharp_{\sigma}} H$ and a smash coproduct structure $A \propto H$ is a Hopf algebra. When $\sigma = \varepsilon_{H} \otimes \varepsilon_{H} \otimes \eta_{A}$, Radford's theorems characterizing the biproduct are obtained and when the antipode of $H$ is a $\sigma$-antipode we find an analogous result with the one due to Wang, Jiao and Zhao.
Citation
J. N. Alonso Alvarez. R. González Rodriguez. J. M. Fernández Vilaboa. "The Hopf algebra structure of a crossed product in a braided monoidal category." Tsukuba J. Math. 26 (2) 299 - 311, December 2002. https://doi.org/10.21099/tkbjm/1496164427
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