Abstract
In this paper, we study the sovereign structure in the category of Doi-Hopf modules. We introduce the notion of the sovereign Doi-Hopf datums and Doi-smash products, and investigate the equivalence of the representations of the Doi-smash products and the category of Doi-Hopf modules. At last, we give a necessary and sufficient condition for the category of Doi-Hopf modules to be a sovereign category. As an application, the sovereign structure in the Yetter-Drinfeld category is discussed.
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