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Better formatting and linking to the abstract page: Strict quantum 2-groups
I assume that you're asking why he needs the equation
(for in the ground Hopf algebra and in the Hopf -algebra ), rather than the entire set-up in that condition; without that set-up (consisting of and themselves), you'd have nothing to talk about.
I don't remember enough about Hopf algebras to answer your question either, but I'm trying to understand it. ☺️
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