A Categorical Approach to Turaev's Hopf Group-Coalgebras
By Stefaan Caenepeel, M. D. Lombaerde. 2004
70 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1e980ae7e5a209c3bcf0651510c5f1394513ff3f
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In Algebra and Number Theory
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Citations in the corpus
- Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category (2005, methodology): “We are ready now to introduce the desired braided T-category (we use terminology as in [18]; for the subject of Turaev categories, see also the original paper of Turaev [16] and [ 2 ], [17]).”
- Monoidal Grothendieck Construction (2018, unknown): “In [CDL06], the authors introduce a category T of Turaev R-modules, as well as a category Z of Zunino R-modules, which serve as symmetric monoidal categories where group-(co)algebras and Hopf group-(co)algebras, [Tur00], live as (co)monoids and Hopf monoids respectively.”