Abstract
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 certain law of their own, which is called the co-pentagon 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.
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