Abstract: Operads, multicategories, and their representations (also called operadic/multicategorical algebras) play a key role in organizing hierarchies of higher homotopies in any category with a good notion of homotopy theory. In this talk we show how one can generalize work of Toen and Rezk to provide a description of the derived category of any multicategorical algebra. Time permitting, we will discuss applications of this theory to problems in combinatorial representation theory.

We do not assume prior knowledge of the theory of operads and multicategories.