摘要
We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the copentagonidentity.We also set up a 2-category of 2-coalgebras.The purpose of this study is from the idea of reconsideringthe quasi-Hopf algebras by the categoriScation process,so that we can study the theory of quasi-Hopf algebras and theirrepresentations in some new framework of higher category theory in naturai ways.
We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on the co-multiplication map and requiring that these isomorphisms satisfy certairl law of their own, which is called the copentagon identity. We also set up a 2-category of 2-coalgebras. The purpose of this study is from the idea of reconsidering the quasi-Hopf algebras by the categorification process, so that we can study the theory of quasi-Hopf algebras and their representations in some new framework of higher category theory in natural ways.
基金
Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 11031005 10871135, 10871227, and PHR201007107
