From Subfactors to Categories and Topology I. Frobenius Algebras in and Morita Equivalence of Tensor Categories
Michael Müger
We consider certain categorical structures that are implicit in subfactor theory. Making the connection between subfactor theory (at finite index) and category theory explicit sheds light on both subjects. Furthermore, it allows various generalizations of these structures, e.g. to arbitrary ground fields, and the proof of new results about topological invariants in three dimensions. The present formalism permits a fairly complete analysis of the quantum double of a semisimple spherical category, which is the subject of a companion paper.