A Lie 2-bialgebra is a Lie 2-algebra equipped with a compatible Lie 2-coalgebra structure. In this paper, we give another equivalent description for Lie2-bialgebras by using the structure maps and compatibility condit...A Lie 2-bialgebra is a Lie 2-algebra equipped with a compatible Lie 2-coalgebra structure. In this paper, we give another equivalent description for Lie2-bialgebras by using the structure maps and compatibility conditions. We can use this method to check whether a 2-term direct sum of vector spaces is a Lie 2-bialgebra easily.展开更多
We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentago...We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.展开更多
文摘A Lie 2-bialgebra is a Lie 2-algebra equipped with a compatible Lie 2-coalgebra structure. In this paper, we give another equivalent description for Lie2-bialgebras by using the structure maps and compatibility conditions. We can use this method to check whether a 2-term direct sum of vector spaces is a Lie 2-bialgebra easily.
基金Acknowledgements The authors would like to thank the referees for a number of helpful comments that greatly improved the presentation of this paper. The first author also thanks Prof. Ke Wu and Prof. Shikun Wang for stimulating discussion and help in preparation of this paper. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11047030, 11171055, 11571145） and the Science and Technology Program of Henan Province （No. 152300410061）.
文摘We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.
