Abstract
We develop a theory of module categories over monoidal categories (this is a straightforward categorization of modules over rings). As applications we show that any semisimple monoidal category with finitely many simple objects is equivalent to the category of representations of a weak Hopf algebra (theorem of T. Hayashi) and we classify module categories over the fusion category of sl(2) at a positive integer level where we meet once again the ADE classification pattern.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ostrik, V. Module categories, weak Hopf algebras and modular invariants. Transformation Groups 8, 177–206 (2003). https://doi.org/10.1007/s00031-003-0515-6
Issue Date:
DOI: https://doi.org/10.1007/s00031-003-0515-6