  We develop abstract nonsense for module categories over monoidal categories
(this is a straightforward categorification 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 classify module categories over the fusion
category of $\hat{sl}(2)$ at a positive integer level where we meet once again
ADE classification pattern.
