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Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2

Gabriella B"ohm·Korn'el Szlach'anyi
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Abstract

We study Frobenius 1-morphisms $ı$ in an additive bicategory $\c$ satisfying the depth 2 condition. We show that the 2-endomorphism rings $\c^2(ı\x\ib,ı\x\ib)$ and $\c^2(\ib\xı,\ib\xı)$ can be equipped with dual Hopf algebroid structures. We prove also that a Hopf algebroid appears as the solution of the above abstract symmetry problem if and only if it possesses a two sided non-degenerate integral.

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Gabriella B"ohm, Korn'el Szlach'anyi. 2003-05-09. Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2. https://arxiv.org/abs/math/0305136

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