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arXiv · 1611.06819

Coquasi-bialgebras with preantipode and rigid monoidal categories

Paolo Saracco
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Abstract

By a theorem of Majid, every monoidal category with a neutral quasi-monoidal functor to finitely-generated and projective $\Bbbk$-modules gives rise to a coquasi-bialgebra. We prove that if the category is also rigid, then the associated coquasi-bialgebra admits a preantipode, providing in this way an analogue for coquasi-bialgebras of Ulbrich's reconstruction theorem for Hopf algebras. When $\Bbbk$ is field, this allows us to characterize coquasi-Hopf algebras as well in terms of rigidity of finite-dimensional corepresentations.

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Paolo Saracco. 2016-11-21. Coquasi-bialgebras with preantipode and rigid monoidal categories. https://doi.org/10.1007/s10468-019-09931-2

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