A Categorical Approach to Turaev's Hopf Group-Coalgebras |
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| Authors: | S Caenepeel M De Lombaerde |
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| Institution: | 1. Faculty of Engineering , Vrije University Brussel, VUB , Brussels, Belgium scaenepe@vub.ac.be;3. Faculty of Engineering , Vrije University Brussel, VUB , Brussels, Belgium |
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| Abstract: | We show that Turaev's group-coalgebras and Hopf group-coalgebras are coalgebras and Hopf algebras in a symmetric monoidal category, which we call the Turaev category. A similar result holds for group-algebras and Hopf group-algebras. As an application, we give an alternative approach to Virelizier's version of the Fundamental Theorem for Hopf algebras. We introduce Yetter–Drinfeld modules over Hopf group-coalgebras using the center construction. |
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| Keywords: | Hopf group coalgebra Hopf module Monoidal category Yetter–Drinfeld module |
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