On Hopf algebras and derived categories

Rozansky-Witten theory is a physical 3d TQFT which depends on a hyperkahler manifold. Roberts and Willerton studying topics related to the partition function of this theory highlighted the relevance of the derived category of coherent sheaves on the hyperkahler manifold. In this talk, I will discuss the Hopf algebra object in the derived category of coherent sheaves motivated by a rigorous construction of an extended TQFT for  Rozansky-Witten theory.