Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2

We study Frobenius 1-morphisms $\text{i}$ in an additive bicategory \c satisfying the depth 2 condition. We show that the 2-endomorphism rings \c^2(\i\x\ib,\i\x\ib) and \c^2(\ib\x\i,\ib\x\i) 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.