Basic Hopf algebras and symmetric bimodules

Motivated by the so-called H-cell reduction theorems, we investigate certain classes of bicategories which have only one apart from possibly identity. We show that H0-simple quasi fiab with unique H0 are fusion categories. further study two non-semisimple quasi-fiab a single The first is , indexed finite-dimensional radically graded basic Hopf algebra A, and second consisting symmetric projective A-A-bimodules. can be viewed as 1-full subbicategory classify simple transitive birepresentations for . point out number equivalence latter finite, while generally not.