If $H$ is a Hopf subalgebra of the Hopf algebra $G$ and $\alpha:V\longrightarrow V\otimes H$ is right corepresentation of $H$ on the vector space $V$ (finite--dimensional), is there a way to induce a corepresentation of $G$ on $V$?
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1$\begingroup$ It looks like the answer is "yes" (see the nlab page here), though I'm not an expert so I don't have any more helpful references. $\endgroup$– Chris GrossackCommented Apr 23 at 21:16
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1$\begingroup$ @ChrisGrossack That would be used to induce a $G$-comodule to an $H$-comodule. Going from $H$ to $G$ is much more straightforward. $\endgroup$– Daniel ArreolaCommented Apr 24 at 1:46
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If $\iota : H \to G$ denotes the inclusion, then $V$ is naturally a $G$-comodule via $(\text{id}_V \otimes \iota) \circ \alpha : V \to V \otimes G$.
