Abstract: In order to study deformations of associative algebras, in 1963, Gerstenhaber constructed operations on the Hochschild complex of an algebra. These operations induce a product and bracket on cohomology, which generalize those on the space of multivector fields over a manifold. This is now known as a Gerstenhaber algebra structure.

Now consider a functor from a small category to a category of algebras. In 1988, Gerstenhaber and Schack showed indirectly that the Hochschild cohomology of such a functor is also a Gerstenhaber algebra. I will describe my efforts to construct operations on the complex that induce this structure.

My motivation comes from algebraic quantum field theory. My methods rely on operad theory.