2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62631We 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.26 pagesQuantum AlgebraCategory Theorytext