A locally rigid semi-Hopf V-category is Hopf and Frobenius if and only if it has non-singular left and right integral families, equivalently if its integral spaces are the monoidal unit.
Larson-Sweedler theorem and the role of grouplike elements in weak Hopf algebras
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A Larson-Sweedler Theorem for Hopf V-Categories
A locally rigid semi-Hopf V-category is Hopf and Frobenius if and only if it has non-singular left and right integral families, equivalently if its integral spaces are the monoidal unit.