FROM SUBFACTORS TO CATEGORIES AND TOPOLOGY I. FROBENIUS ALGEBRAS IN AND MORITA EQUIVALENCE OF

TENSOR CATEGORIES

MICHAEL MÜGER

Abstract. 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.