We present a skein-theoretic construction based on a graphical calculus for pivotal bicategories, which can be applied in particular to a pivotal monoidal category and the bicategory of Frobenius algebras internal to it. The relationship between these structures induces an isomorphism between their respective skein modules, encoding information about CFT correlators and their mapping class group actions.
(Work with Jürgen Fuchs and Yang Yang.)