摘要: We use a version of Haboush's theorem over complete local Noetherian rings to prove faithfulness the lifting for semisimple cosemisimple Hopf algebras and separable (braided, symmetric) fusion categories from characteristic $p$ zero (arXiv/math:0203060, Section 9), showing that, moreover, any isomorphism between such structures can be reduced modulo $p$. This fills gap in arXiv/math:0203060, Subsection 9.3. also show that is fully faithful functor, induces an on Picard Brauer-Picard groups. Finally, we subcategory or quotient category multifusion (resolving open question 9.4), this certain classes tensor functors lifts
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